Calculus For Biology and Medicine 4th Edition Neuhauser Solutions Manual

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Calculus For Biology and Medicine 4th Edition Neuhauser Solutions Manual.

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Product Details:

  • ISBN-10 ‏ : ‎ 0134070046
  • ISBN-13 ‏ : ‎ 978-0134070049
  • Author:  Claudia Neuhauser, Marcus Roper,

Calculus for Biology and Medicine motivates life and health science majors to learn calculus through relevant and strategically placed applications to their chosen fields. It presents the calculus in such a way that the level of rigor can be adjusted to meet the specific needs of the audience ― from a purely applied course to one that matches the rigor of the standard calculus track.

 

Table of Content:

  1. Calculus for Biology and Medicine
  2. Contents
  3. Preface
  4. New to This Edition
  5. Features of the Text
  6. Reflections and Outlook
  7. Chapter Summary
  8. How to Use This Book
  9. MyLab Math Online Course (access code required)
  10. Supplements
  11. Derivatives and Integrals
  12. Basic Differentiation Rules
  13. Basic Integration Formulas
  14. Algebra
  15. Quadratic Formula
  16. Factorial notation
  17. Radicals
  18. Exponents
  19. Binomial Formula
  20. Special Factors
  21. Geometry
  22. Distance Formulas
  23. Equations of Lines and Circles
  24. Areas and Volumes
  25. Trigonometry
  26. Definition of the Six Trigonometric Functions
  27. MyLab Math for Calculus for Biology and Medicine, 4e (access code required)
  28. Exercises with Immediate Feedback
  29. Complete eText
  30. Questions that Deepen Understanding
  31. Chapter 1 Preview and Review
  32. A Brief Overview of Calculus
  33. Section 1.1 Precalculus Skills Diagnostic Test
  34. 1.2 Preliminaries
  35. 1.2.1 The Real Numbers
  36. Solution
  37. Solution
  38. Solution
  39. 1.2.2 Lines in the Plane
  40. Solution
  41. Solution
  42. 1.2.3 Equation of the Circle
  43. Solution
  44. 1.2.4 Trigonometry
  45. Solution
  46. 1.2.5 Exponentials and Logarithms
  47. Solution
  48. Solution
  49. Solution
  50. Solution
  51. 1.2.6 Complex Numbers and Quadratic Equations
  52. Solution
  53. Solution
  54. Solution
  55. Solution
  56. Section 1.2 Problems
  57. 1.2.1
  58. 1.2.2
  59. 1.2.3
  60. 1.2.4
  61. 1.2.5
  62. 1.2.6
  63. 1.3 Elementary Functions
  64. 1.3.1 What Is a Function?
  65. Solution
  66. Solution
  67. Solution
  68. 1.3.2 Polynomial Functions
  69. Solution
  70. Solution
  71. 1.3.3 Rational Functions
  72. Solution
  73. 1.3.4 Power Functions
  74. 1.3.5 Exponential Functions
  75. Solution
  76. 1.3.6 Inverse Functions
  77. Solution
  78. Geometric Relationship Between f(x) and f−1(x)
  79. 1.3.7 Logarithmic Functions
  80. Solution
  81. Solution
  82. Solution
  83. 1.3.8 Trigonometric Functions
  84. Solution
  85. Section 1.3 Problems
  86. 1.3.1
  87. 1.3.2
  88. 1.3.3
  89. 1.3.4
  90. 1.3.5
  91. 1.3.6
  92. 1.3.7
  93. 1.3.8
  94. 1.4 Graphing
  95. 1.4.1 Graphing and Basic Transformations of Functions
  96. Solution
  97. Solution
  98. 1.4.2 The Logarithmic Scale
  99. Solution
  100. 1.4.3 Transformations into Linear Functions
  101. Exponential Functions
  102. Solution
  103. Solution
  104. Power Functions
  105. Solution
  106. Solution
  107. Applications
  108. Solution
  109. Solution
  110. Solution
  111. 1.4.4 From a Verbal Description to a Graph
  112. Section 1.4 Problems
  113. 1.4.1
  114. 1.4.2
  115. 1.4.3
  116. 1.4.4
  117. Chapter 1 Review
  118. Key Terms
  119. Review Problems
  120. Chapter 2 Discrete-Time Models, Sequences, and Difference Equations
  121. 2.1 Exponential Growth and Decay
  122. 2.1.1 Modeling Population Growth in Discrete Time
  123. Solution
  124. 2.1.2 Recurrence Equations
  125. 2.1.3 Visualizing Recurrence Equations
  126. Nt+1 Against Nt
  127. Reproductive Rate Against Nt
  128. Section 2.1 Problems
  129. 2.1.1
  130. 2.1.2
  131. 2.1.3
  132. 2.2 Sequences
  133. 2.2.1 What Are Sequences?
  134. Solution
  135. Solution
  136. Solution
  137. 2.2.2 Using Spreadsheets to Calculate a Recursive Sequence
  138. 2.2.3 Limits
  139. Solution
  140. Solution
  141. Solution
  142. Solution
  143. Formal Definition of Limits
  144. Solution
  145. Limit Laws
  146. Solution
  147. Solution
  148. 2.2.4 Recurrence Equations
  149. Solution
  150. Solution
  151. Solution
  152. 2.2.5 Using Σ Notation to Represent Sums of Sequences
  153. Solution
  154. Section 2.2 Problems
  155. 2.2.1
  156. 2.2.2
  157. 2.2.3
  158. Formal Definition of Limits:
  159. Formal Definition of Limits:
  160. 2.2.4
  161. 2.2.5
  162. 2.3 Modeling with Recurrence Equations
  163. 2.3.1 Density-Dependent Population Growth
  164. Solution
  165. Solution
  166. 2.3.2 Density-Dependent Population Growth: The Beverton-Holt Model
  167. Solution
  168. 2.3.3 The Discrete Logistic Equation
  169. 2.3.4 Modeling Drug Absorption
  170. Solution
  171. Solution
  172. Section 2.3 Problems
  173. 2.3.1
  174. 2.3.2
  175. 2.3.3
  176. 2.3.4
  177. Chapter 2 Review
  178. Key Terms
  179. Review Problems
  180. Chapter 3 Limits and Continuity
  181. 3.1 Limits
  182. 3.1.1 A Non-Rigorous Discussion of Limits
  183. Solution
  184. Solution
  185. Solution
  186. Solution
  187. Solution
  188. 3.1.2 Pitfalls of Finding Limits
  189. Solution
  190. Solution
  191. Solution
  192. Solution
  193. 3.1.3 Limit Laws
  194. Solution
  195. Solution
  196. Solution
  197. Solution
  198. Solution
  199. Solution
  200. Section 3.1 Problems
  201. 3.1.1 and 3.1.2
  202. 3.1.3
  203. 3.2 Continuity
  204. 3.2.1 What Is Continuity?
  205. Solution
  206. Solution
  207. Solution
  208. Solution
  209. Solution
  210. 3.2.2 Combinations of Continuous Functions
  211. Proof
  212. Solution
  213. Solution
  214. Solution
  215. Solution
  216. Solution
  217. Solution
  218. Section 3.2 Problems
  219. 3.2.1
  220. 3.2.2
  221. 3.3 Limits at Infinity
  222. Solution
  223. Solution
  224. Section 3.3 Problems
  225. 3.4 Trigonometric Limits and the Sandwich Theorem
  226. 3.4.1 Geometric Argument for Trigonometric Limits
  227. Proof that limx→01−cos⁡xx=0
  228. Solution
  229. 3.4.2 The Sandwich Theorem
  230. Solution
  231. Solution
  232. Proof that limx→0sin⁡xx=1
  233. Section 3.4 Problems
  234. 3.4.1
  235. 3.4.2
  236. 3.5 Properties of Continuous Functions
  237. 3.5.1 The Intermediate-Value Theorem and The Bisection Method
  238. Solution
  239. Solution
  240. 3.5.2 Using a Spreadsheet to Implement the Bisection Method
  241. 3.5.3 A Final Remark on Continuous Functions
  242. Section 3.5 Problems
  243. 3.5.1
  244. 3.5.2
  245. 3.6 A Formal Definition of Limits
  246. Solution
  247. Solution
  248. Solution
  249. Solution
  250. Solution
  251. Solution
  252. Section 3.6 Problems
  253. Chapter 1 Review
  254. Key Terms
  255. Review Problems
  256. Chapter 4 Differentiation
  257. 4.1 Formal Definition of the Derivative
  258. Solution
  259. Section 4.1 Problems
  260. 4.2 Properties of the Derivative
  261. 4.2.1 Interpreting the Derivative
  262. Velocity.
  263. Population Growth
  264. The Rate of a Chemical Reaction
  265. 4.2.2 Differentiability and Continuity
  266. Proof
  267. Solution
  268. Section 4.2 Problems
  269. 4.2.1
  270. 4.2.2
  271. 4.3 The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials
  272. Section 4.3 Problems
  273. 4.4 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions
  274. 4.4.1 The Product Rule
  275. Proof
  276. Solution
  277. Solution
  278. Solution
  279. Solution
  280. 4.4.2 The Quotient Rule
  281. Solution
  282. Solution
  283. Proof
  284. Solution
  285. Solution
  286. Solution
  287. Solution
  288. Solution
  289. Section 4.4 Problems
  290. 4.4.1
  291. 4.4.2
  292. 4.5 The Chain Rule
  293. 4.5.1 The Chain Rule
  294. Solution
  295. Solution
  296. Solution
  297. Solution
  298. Solution
  299. Proof of the Quotient Rule
  300. Solution
  301. Solution
  302. Solution
  303. Solution
  304. Solution
  305. Solution
  306. 4.5.2 Proof of the Chain Rule
  307. Proof of the Chain Rule
  308. Section 4.5 Problems
  309. 4.5.1
  310. 4.6 Implicit Functions and Implicit Differentiation
  311. 4.6.1 Implicit Differentiation
  312. Solution
  313. Solution
  314. Solution
  315. Proof of the Power Rule for Rational Exponents
  316. 4.6.2 Related Rates
  317. Solution
  318. Solution
  319. Solution
  320. Section 4.6 Problems
  321. 4.6.1
  322. 4.6.2
  323. 4.7 Higher Derivatives
  324. Solution
  325. Solution
  326. Solution
  327. Solution
  328. Solution
  329. Section 4.7 Problems
  330. 4.7
  331. 4.8 Derivatives of Trigonometric Functions
  332. Section 4.8 Problems
  333. 4.9 Derivatives of Exponential Functions
  334. Solution
  335. Solution
  336. Solution
  337. Solution
  338. Solution
  339. Solution
  340. Section 4.9 Problems
  341. 4.10 Derivatives of Inverse Functions, Logarithmic Functions, and the Inverse Tangent Function
  342. 4.10.1 Derivatives of Inverse Functions
  343. Solution
  344. Solution
  345. Solution
  346. Solution
  347. 4.10.2 The Derivative of the Logarithmic Function
  348. Solution
  349. Solution
  350. Solution
  351. Solution
  352. Solution
  353. Solution
  354. 4.10.3 Logarithmic Differentiation
  355. Solution
  356. Solution
  357. Proof
  358. Section 4.10 Problems
  359. 4.10.1
  360. 4.10.2
  361. 4.10.3
  362. 4.11 Linear Approximation and Error Propagation
  363. Solution
  364. Solution
  365. Solution
  366. Solution
  367. Section 4.11 Problems
  368. Chapter 4 Review
  369. Key Terms
  370. Review Problems
  371. Chapter 5 Applications of Differentiation
  372. 5.1 Extrema and the Mean-Value Theorem
  373. 5.1.1 The Extreme-Value Theorem
  374. Solution
  375. Solution
  376. Solution
  377. 5.1.2 Local Extrema
  378. Solution
  379. Solution
  380. Proof
  381. Solution
  382. 5.1.3 The Mean-Value Theorem
  383. Solution
  384. Proof of Rolle’s Theorem
  385. Proof of the MVT
  386. Solution
  387. Solution
  388. Proof of Corollary 2
  389. Solution
  390. Section 5.1 Problems
  391. 5.1.1
  392. 5.1.2
  393. 5.1.3
  394. 5.2 Monotonicity and Concavity
  395. 5.2.1 Monotonicity
  396. Proof
  397. Solution
  398. Solution
  399. 5.2.2 Concavity
  400. Proof
  401. Solution
  402. Solution
  403. Section 5.2 Problems
  404. 5.2.1 and 5.2.2
  405. 5.3 Extrema and Inflection Points
  406. 5.3.1 Extrema
  407. Solution
  408. Solution
  409. Solution
  410. 5.3.2 Inflection Points
  411. Solution
  412. Section 5.3 Problems
  413. 5.3.1
  414. 5.3.2
  415. 5.4 Optimization
  416. Solution
  417. Solution
  418. Solution
  419. Solution
  420. Solution
  421. Section 5.4 Problems
  422. 5.5 L’Hôpital’s Rule
  423. Solution
  424. Solution
  425. Solution
  426. Solution
  427. Solution
  428. Solution
  429. 0 ⋅ ∞
  430. Solution
  431. Solution
  432. ∞−∞
  433. Solution
  434. Solution
  435. 00, 1∞, ∞0
  436. Solution
  437. Solution
  438. Section 5.5 Problems
  439. 5.6 Graphing and Asymptotes
  440. Solution
  441. Solution
  442. Solution
  443. Solution
  444. Solution
  445. Section 5.6 Problems
  446. 5.7 Recurrence Equations: Stability
  447. 5.7.1 Exponential Growth
  448. Cobwebbing
  449. 5.7.2 Stability: General Case
  450. Stability
  451. Proof
  452. Solution
  453. Solution
  454. 5.7.3 Population Growth Models
  455. Solution
  456. Solution
  457. Section 5.7 Problems
  458. 5.8 Numerical Methods: The Newton–Raphson Method
  459. Solution
  460. Solution
  461. Solution
  462. Solution
  463. Section 5.8 Problems
  464. 5.9 Modeling Biological Systems Using Differential Equations
  465. 5.9.1 Modeling Population Growth
  466. 5.9.2 Interpreting the Mathematical Model
  467. Solution
  468. Solution
  469. 5.9.3 Passage of Drugs Through the Human Body
  470. Solution
  471. Solution
  472. Section 5.9 problems
  473. 5.9.1 and 5.9.2
  474. 5.9.3
  475. 5.10 Antiderivatives
  476. Section 5.10 problems
  477. Chapter 5 Review
  478. Key Terms
  479. Review Problems
  480. Chapter 6 Integration
  481. 6.1 The Definite Integral
  482. 6.1.1 The Area Problem
  483. 6.1.2 The General Theory of Riemann Integrals
  484. Solution
  485. Solution
  486. Solution
  487. Solution
  488. Geometric Interpretation of Definite Integrals
  489. Solution
  490. Solution
  491. Solution
  492. 6.1.3 Properties of the Riemann Integral
  493. Proof of (4)
  494. Proof of (5).
  495. Solution
  496. 6.1.4 Order Properties of the Riemann Integral
  497. Solution
  498. Solution
  499. Section 6.1 Problems
  500. 6.1.1
  501. 6.1.2
  502. 6.1.3
  503. 6.1.4
  504. 6.2 The Fundamental Theorem of Calculus
  505. 6.2.1 The Fundamental Theorem of Calculus (Part I)
  506. Solution
  507. Solution
  508. 6.2.2 Leibniz’s Rule and a Rigorous Proof of the Fundamental Theorem of Calculus
  509. Leibniz’s Rule
  510. Solution
  511. Solution
  512. Solution
  513. Proof of the Fundamental Theorem of Calculus (Part I) (Optional)
  514. 6.2.3 Antiderivatives and Indefinite Integrals
  515. Solution
  516. Solution
  517. Solution
  518. Solution
  519. Solution
  520. Solution
  521. 6.2.4 The Fundamental Theorem of Calculus (Part II)
  522. Using the FTC (Part II) to Evaluate Definite Integrals.
  523. Solution
  524. Solution
  525. Solution
  526. Solution
  527. Solution
  528. Finding an Integrand
  529. Solution
  530. Solution
  531. Discontinuous Integrand
  532. Solution
  533. Section 6.2 Problems
  534. 6.2.1
  535. 6.2.2
  536. 6.2.3
  537. 6.2.4
  538. 6.3 Applications of Integration
  539. 6.3.1 Cumulative Change
  540. Solution
  541. Solution
  542. Solution
  543. 6.3.2 Average Values
  544. Solution
  545. Solution
  546. Solution
  547. 6.3.3 The Mean-Value Theorem
  548. Solution
  549. Solution
  550. Proof of the Mean-Value Theorem for Definite Integrals
  551. 6.3.4 Areas
  552. Solution
  553. Solution
  554. Solution
  555. 6.3.5 The Volume of a Solid
  556. Solution
  557. Solution
  558. Solution
  559. Solution
  560. 6.3.6 Rectification of Curves
  561. Solution
  562. Solution
  563. Solution
  564. Section 6.3 Problems
  565. 6.3.1
  566. 6.3.2
  567. 6.3.3
  568. 6.3.4
  569. 6.3.5
  570. 6.3.6
  571. Chapter 6 Review
  572. Key Terms
  573. Review Problems
  574. Chapter 7 Integration Techniques and Computational Methods
  575. 7.1 The Substitution Rule
  576. 7.1.1 Indefinite Integrals
  577. Solution
  578. Solution
  579. Solution
  580. Solution
  581. Solution
  582. Solution
  583. Solution
  584. 7.1.2 Definite Integrals
  585. First Way
  586. Second Way
  587. Solution
  588. Solution
  589. Solution
  590. Solution
  591. Solution
  592. Section 7.1 Problems
  593. 7.1.1
  594. 7.1.2
  595. 7.2 Integration by Parts and Practicing Integration
  596. 7.2.1 Integration by Parts
  597. Solution
  598. Solution
  599. Solution
  600. Solution
  601. Solution
  602. Solution
  603. Solution
  604. 7.2.2 Practicing Integration
  605. Solution
  606. Solution
  607. Solution
  608. Section 7.2 Problems
  609. 7.2.1
  610. 7.2.2
  611. 7.3 Rational Functions and Partial Fractions
  612. 7.3.1 Proper Rational Functions
  613. Solution
  614. Solution
  615. 7.3.2 Partial-Fraction Decomposition
  616. First Method
  617. Second Method
  618. Solution
  619. Solution
  620. Solution
  621. 7.3.3 Repeated Linear Factors
  622. Solution
  623. Solution
  624. 7.3.4 Irreducible Quadratic Factors
  625. Solution
  626. Solution
  627. Solution
  628. Solution
  629. 7.3.5 Summary
  630. Case 1a: Q(x) is a product of two distinct linear factors.
  631. Case 1b: Q(x) is a product of two identical linear factors.
  632. Case 2: (Optional) Q(x) is an irreducible quadratic polynomial.
  633. Section 7.3 Problems
  634. 7.3.1
  635. 7.3.2
  636. 7.3.3
  637. 7.3.4
  638. 7.3.5
  639. 7.4 Improper Integrals
  640. 7.4.1 Type 1: Unbounded Intervals
  641. Solution
  642. Solution
  643. Solution
  644. Solution
  645. Solution
  646. 7.4.2 Type 2: Unbounded Integrand
  647. Solution
  648. Solution
  649. Solution
  650. 7.4.3 A Comparison Result for Improper Integrals
  651. Solution
  652. Solution
  653. Section 7.4 Problems
  654. 7.4.1, 7.4.2
  655. 7.4.3
  656. 7.5 Numerical Integration
  657. 7.5.1 The Midpoint Rule
  658. Solution
  659. Solution
  660. 7.5.2 The Trapezoidal Rule
  661. Solution
  662. Solution
  663. 7.5.3 Using a Spreadsheet for Numerical Integration
  664. Solution
  665. 7.5.4 Estimating Error in a Numerical Integration
  666. Section 7.5 Problems
  667. Sections 7.5.1, 7.5.2
  668. 7.5.3
  669. 7.5.4
  670. 7.6 The Taylor Approximation
  671. 7.6.1 Taylor Polynomials
  672. Solution
  673. Solution
  674. Solution
  675. Solution
  676. 7.6.2 The Taylor Polynomial about x=a
  677. Solution
  678. 7.6.3 How Accurate Is the Approximation?
  679. Solution
  680. Solution
  681. Section 7.6 Problems
  682. 7.6.1
  683. 7.6.2
  684. 7.6.3
  685. 7.7 Tables of Integrals
  686. Solution
  687. Solution
  688. Solution
  689. Solution
  690. Solution
  691. Solution
  692. Section 7.7 Problems
  693. Chapter 7 Review
  694. Key Terms
  695. Review Problems
  696. Chapter 8 Differential Equations
  697. 8.1 Solving Separable Differential Equations
  698. 8.1.1 Pure-Time Differential Equations
  699. Solution
  700. 8.1.2 Autonomous Differential Equations
  701. Solution
  702. Solution
  703. Solution
  704. Solution
  705. 8.1.3 General Separable Equations
  706. Solution
  707. Section 8.1 Problems
  708. 8.1.1
  709. 8.1.2
  710. 8.1.3
  711. 8.2 Equilibria and Their Stability
  712. 8.2.1 Equilibrium Points
  713. Solution
  714. Solution
  715. 8.2.2 Graphical Approach to Finding Equilibria
  716. 8.2.3 Stability of Equilibrium Points
  717. Solution
  718. Solution
  719. Solution
  720. Solution
  721. Solution
  722. 8.2.4 Sketching Solutions Using the Vector Field Plot
  723. Solution
  724. Solution
  725. 8.2.5 Behavior Near an Equilibrium
  726. Solution
  727. Section 8.2 Problems
  728. 8.2.1
  729. 8.2.2, 8.2.3
  730. 8.2.4
  731. 8.2.5
  732. 8.3 Differential Equation Models
  733. 8.3.1 Compartment Models
  734. 8.3.2 An Ecological Model
  735. 8.3.3 Modeling a Chemical Reaction
  736. 8.3.4 The Evolution of Cooperation
  737. 8.3.5 Epidemic Model
  738. Section 8.3 Problems
  739. 8.3.1
  740. 8.3.2
  741. 8.3.3
  742. 8.3.4
  743. 8.3.5
  744. 8.4 Integrating Factors and Two-Compartment Models
  745. 8.4.1 Integrating Factors
  746. Solution
  747. Solution
  748. Solution
  749. Solution
  750. 8.4.2 Two-Compartment Models
  751. Solution
  752. Solution
  753. Section 8.4 Problems
  754. 8.4.1
  755. 8.4.2
  756. Chapter 8 Review
  757. Key Terms
  758. Review Problems
  759. Chapter 9 Linear Algebra and Analytic Geometry
  760. 9.1 Linear Systems
  761. 9.1.1 Graphical Solution
  762. Solution
  763. Solution
  764. Solution
  765. 9.1.2 Solving Equations Using Elimination
  766. Solution
  767. 9.1.3 Solving Systems of Linear Equations
  768. Solution
  769. Solution
  770. Solution
  771. Solution
  772. 9.1.4 Representing Systems of Equations Using Matrices
  773. Solution
  774. Solution
  775. Solution
  776. Solution
  777. Section 9.1 Problems
  778. 9.1.1, 9.1.2
  779. 9.1.3
  780. 9.1.4
  781. 9.2 Matrices
  782. 9.2.1 Matrix Operations
  783. Solution
  784. Solution
  785. Solution
  786. 9.2.2 Matrix Multiplication
  787. Solution
  788. Solution
  789. Solution
  790. Solution
  791. Solution
  792. 9.2.3 Inverse Matrices
  793. Solution
  794. Solution
  795. Solution
  796. Solution
  797. Solution
  798. Solution
  799. 9.2.4 Computing Inverse Matrices
  800. Solution
  801. Solution
  802. Section 9.2 Problems
  803. 9.2.1, 9.2.2
  804. 9.2.3
  805. 9.2.4
  806. 9.3 Linear Maps, Eigenvectors, and Eigenvalues
  807. 9.3.1 Graphical Representation
  808. Vectors
  809. Solution
  810. Solution
  811. Linear Maps
  812. Solution
  813. 9.3.2 Eigenvalues and Eigenvectors
  814. Solution
  815. Solution
  816. Solution
  817. Solution
  818. Solution
  819. Solution
  820. 9.3.3 Iterated Maps (Needed for Section 9.4 and 10.9)
  821. Solution
  822. Section 9.3 Problems
  823. 9.3.1
  824. 9.3.2
  825. 9.3.3
  826. 9.4 Demographic Modeling
  827. 9.4.1 Modeling with Leslie Matrices
  828. Solution
  829. Solution
  830. 9.4.2 Stable Age Distributions in Demographic Models
  831. Solution
  832. Solution
  833. Section 9.4 Problems
  834. 9.4.1
  835. 9.4.2
  836. 9.5 Analytic Geometry
  837. 9.5.1 Points and Vectors in Higher Dimensions
  838. Vector Representation
  839. Solution
  840. Length of a Vector
  841. Solution
  842. Solution
  843. 9.5.2 The Dot Product
  844. Solution
  845. The Angle between Two Vectors
  846. Solution
  847. Solution
  848. Solution
  849. Lines in the Plane
  850. Solution
  851. Planes in R3
  852. Solution
  853. 9.5.3 Parametric Equations of Lines
  854. Solution
  855. Solution
  856. Solution
  857. Solution
  858. Section 9.5 Problems
  859. 9.5.1
  860. 9.5.2
  861. 9.5.3
  862. Chapter 9 Review
  863. Key Terms
  864. Review Problems
  865. Chapter 10 Multivariate Calculus
  866. 10.1 Functions of Two or More Independent Variables
  867. 10.1.1 Defining a Function of Two or More Variables
  868. Solution
  869. Solution
  870. Solution
  871. 10.1.2 The Graph of a Function of Two Independent Variables-Surface Plot
  872. 10.1.3 Heat Maps
  873. Solution
  874. 10.1.4 Contour Plots
  875. Solution
  876. Solution
  877. Section 10.1 Problems
  878. 10.1.1
  879. 10.1.2
  880. 10.1.3
  881. 10.1.4
  882. 10.2 Limits and Continuity
  883. 10.2.1 Informal Definition of Limits
  884. Limits of Polynomials When the Limits Exist.
  885. Limits of Rational Functions When the Limits Exist.
  886. Limits That Do Not Exist.
  887. Solution
  888. Solution
  889. 10.2.2 Continuity
  890. Solution
  891. Composition of Functions.
  892. 10.2.3 Formal Definition of Limits
  893. Solution
  894. Section 10.2 Problems
  895. 10.2.1
  896. 10.2.2
  897. 10.2.3
  898. 10.3 Partial Derivatives
  899. 10.3.1 Functions of Two Variables
  900. Solution
  901. Solution
  902. Geometric Interpretation.
  903. Solution
  904. A Biological Application — Prey Capture
  905. 10.3.2 Functions of More Than Two Variables
  906. Solution
  907. 10.3.3 Higher-Order Partial Derivatives
  908. Solution
  909. Section 10.3 Problems
  910. 10.3.1
  911. 10.3.2
  912. 10.3.3
  913. 10.4 Tangent Planes, Differentiability, and Linearization
  914. 10.4.1 Functions of Two Variables
  915. Tangent Planes.
  916. Solution
  917. Differentiability.
  918. Solution
  919. Solution
  920. Linearization.
  921. Solution
  922. Solution
  923. 10.4.2 Vector-Valued Functions
  924. Solution
  925. Solution
  926. Solution
  927. Solution
  928. Section 10.4 Problems
  929. 10.4.1
  930. 10.4.2
  931. 10.5 The Chain Rule and Implicit Differentiation
  932. 10.5.1 The Chain Rule for Functions of Two Variables
  933. Solution
  934. Solution
  935. Solution
  936. 10.5.2 Implicit Differentiation
  937. Solution
  938. Solution
  939. Section 10.5 Problems
  940. 10.5.1
  941. 10.5.2
  942. 10.6 Directional Derivatives and Gradient Vectors
  943. 10.6.1 Deriving the Directional Derivative
  944. Deriving the Directional Derivative Using the Chain Rule.
  945. Deriving the Directional Derivative Without Using the Chain Rule.
  946. Solution
  947. Solution
  948. 10.6.2 Properties of the Gradient Vector
  949. Solution
  950. Solution
  951. Section 10.6 Problems
  952. 10.6
  953. 10.7 Maximization and Minimization of Functions
  954. 10.7.1 Local Maxima and Minima
  955. Solution
  956. Solution
  957. Solution
  958. Solution
  959. A Sufficient Condition Based on Eigenvalues (Optional).
  960. Solution
  961. Solution
  962. Solution
  963. 10.7.2 Global Extrema
  964. Solution
  965. Solution
  966. Solution
  967. 10.7.3 Extrema with Constraints
  968. Solution
  969. Solution
  970. Solution
  971. Solution
  972. 10.7.4 Least-Squares Data Fitting
  973. Solution
  974. Solution
  975. Section 10.7 Problems
  976. 10.7.1 and 10.7.2
  977. 10.7.3
  978. 10.7.4
  979. 10.8 Diffusion
  980. Section 10.8 Problems
  981. 10.8
  982. 10.9 Systems of Recurrence Equations *
  983. 10.9.1 A Biological Example
  984. 10.9.2 Equilibria and Stability in Systems of Linear Recurrence Equations
  985. Solution
  986. Solution
  987. 10.9.3 Equilibria and Stability of Nonlinear Systems of Recurrence Equations
  988. Solution
  989. Solution
  990. Solution
  991. Solution
  992. Section 10.9 Problems
  993. 10.9.1
  994. 10.9.2
  995. 10.9.3
  996. Chapter 10 Review
  997. Key Terms
  998. Review Problems
  999. Chapter 11 Systems of Differential Equations
  1000. 11.1 Linear Systems: Theory
  1001. Solution
  1002. 11.1.1 The Vector Field
  1003. 11.1.2 Solving Linear Systems
  1004. Specific Solutions.
  1005. The General Solution.
  1006. Solution
  1007. 11.1.3 Equilibria and Stability
  1008. 11.1.4 Systems with Complex Conjugate Eigenvalues
  1009. Where Do the Oscillations Come From?
  1010. Solution
  1011. 11.1.5 Summary of the Theory of Linear Systems
  1012. Section 11.1 Problems
  1013. 11.1.1
  1014. 11.1.2
  1015. 11.1.3
  1016. 11.1.4
  1017. 11.1.5
  1018. 11.2 Linear Systems: Applications
  1019. 11.2.1 Two-Compartment Models
  1020. Solving the system when c=d=0
  1021. Solution
  1022. Solution
  1023. Solution
  1024. 11.2.2 A Mathematical Model for Love
  1025. 11.2.3 The Harmonic Oscillator
  1026. Section 11.2 Problems
  1027. 11.2.1
  1028. 11.2.2
  1029. 11.2.3
  1030. 11.3 Nonlinear Autonomous Systems: Theory
  1031. 11.3.1 Analytical Approach
  1032. A Single Autonomous Differential Equation.
  1033. Solution
  1034. Systems of Two Differential Equations.
  1035. Solution
  1036. Solution
  1037. 11.3.2 Graphical Approach for 2×2 Systems
  1038. Solution
  1039. Section 11.3 Problems
  1040. 11.3.1
  1041. 11.3.2
  1042. 11.4 Nonlinear Systems: Lotka–Volterra Model for Interspecific Interactions
  1043. 11.4.1 Competition
  1044. Zero Isoclines.
  1045. Interpreting the Conditions for Coexistence.
  1046. Linearization.
  1047. 11.4.2 A Predator–Prey Model
  1048. Section 11.4 Problems
  1049. 11.4.1
  1050. 11.4.2
  1051. 11.5 More Mathematical Models
  1052. 11.5.1 The Community Matrix
  1053. Mutualism
  1054. Competition
  1055. Commensalism and Amensalism
  1056. Predation
  1057. 11.5.2 Neuron Activity
  1058. 11.5.3 Enzymatic Reactions
  1059. 11.5.4 Microbial Growth in a Chemostat
  1060. 11.5.5 A Model for Epidemics
  1061. Solution
  1062. Solution
  1063. Section 11.5 Problems
  1064. 11.5.1
  1065. 11.5.2
  1066. 11.5.3
  1067. 11.5.4
  1068. 11.5.5
  1069. Lethal Diseases
  1070. Relapsing Infections
  1071. Chapter 11 Review
  1072. Key Terms
  1073. Review Problems
  1074. Chapter 12 Probability and Statistics
  1075. 12.1 Counting
  1076. 12.1.1 The Multiplication Principle
  1077. Solution
  1078. Solution
  1079. 12.1.2 Permutations
  1080. Solution
  1081. Solution
  1082. Solution
  1083. 12.1.3 Combinations
  1084. Solution
  1085. Solution
  1086. 12.1.4 Combining the Counting Principles
  1087. Solution
  1088. Solution
  1089. Solution
  1090. Solution
  1091. Solution
  1092. Solution
  1093. Section 12.1 Problems
  1094. 12.1.1
  1095. 12.1.2
  1096. 12.1.3
  1097. 12.1.4
  1098. 12.2 What Is Probability?
  1099. 12.2.1 Basic Definitions
  1100. Basic Set Operations
  1101. Solution
  1102. The Definition of Probability
  1103. Solution
  1104. Solution
  1105. 12.2.2 Equally Likely Outcomes
  1106. Solution
  1107. Solution
  1108. Solution
  1109. An Application from Genetics
  1110. Solution
  1111. The Mark–Recapture Method
  1112. Solution
  1113. Solution
  1114. Solution
  1115. Section 12.2 Problems
  1116. 12.2.1
  1117. 12.2.2
  1118. Color Blindness
  1119. 12.3 Conditional Probability and Independence
  1120. 12.3.1 Conditional Probability
  1121. Solution
  1122. Solution
  1123. 12.3.2 The Law of Total Probability
  1124. Solution
  1125. Solution
  1126. 12.3.3 Independence
  1127. Solution
  1128. Solution
  1129. Solution
  1130. Solution
  1131. 12.3.4 The Bayes Formula
  1132. Section 12.3 Problems
  1133. 12.3.1
  1134. 12.3.2
  1135. 12.3.3
  1136. 12.3.4
  1137. 12.4 Discrete Random Variables and Discrete Distributions
  1138. 12.4.1 Discrete Distributions
  1139. Solution
  1140. Solution
  1141. 12.4.2 Mean and Variance
  1142. The Average Value, or the Mean, of a Discrete Random Variable
  1143. Solution
  1144. The Variance of a Discrete Random Variable
  1145. Solution
  1146. Solution
  1147. Solution
  1148. Solution
  1149. Solution
  1150. Joint Distributions
  1151. Solution
  1152. Solution
  1153. Solution
  1154. Solution
  1155. Solution
  1156. 12.4.3 The Binomial Distribution
  1157. Solution
  1158. Solution
  1159. Down Syndrome
  1160. Solution
  1161. Solution
  1162. Solution
  1163. Sampling With and Without Replacement.
  1164. Solution
  1165. Solution
  1166. 12.4.4 The Multinomial Distribution
  1167. Solution
  1168. Solution
  1169. 12.4.5 Geometric Distribution
  1170. Solution
  1171. Solution
  1172. Solution
  1173. Solution
  1174. Solution
  1175. 12.4.6 The Poisson Distribution
  1176. Solution
  1177. Solution
  1178. Solution
  1179. Solution
  1180. Solution
  1181. Section 12.4 Problems
  1182. 12.4.1
  1183. 12.4.2
  1184. 12.4.3
  1185. 12.4.4
  1186. 12.4.5
  1187. 12.4.6
  1188. 12.5 Continuous Distributions
  1189. 12.5.1 Density Functions
  1190. Solution
  1191. Solution
  1192. Solution
  1193. Seed Dispersal
  1194. Solution
  1195. 12.5.2 The Normal Distribution
  1196. Solution
  1197. Solution
  1198. Solution
  1199. Using the Table to Find Probabilities
  1200. Solution
  1201. Solution
  1202. Solution
  1203. A Note on Samples
  1204. Solution
  1205. 12.5.3 The Uniform Distribution
  1206. Solution
  1207. Solution
  1208. 12.5.4 The Exponential Distribution
  1209. Solution
  1210. Solution
  1211. Radioactive Decay
  1212. Solution
  1213. Seed Dispersal
  1214. Solution
  1215. Solution
  1216. 12.5.5 The Poisson Process
  1217. Continuation of Example 14
  1218. Solution
  1219. 12.5.6 Aging
  1220. Non-aging
  1221. Solution
  1222. Aging
  1223. Solution
  1224. Fruit Fly Lifetimes
  1225. Solution
  1226. Section12.5 Problems
  1227. 12.5.1
  1228. 12.5.2
  1229. 12.5.3
  1230. 12.5.4
  1231. 12.5.5
  1232. 12.5.6
  1233. 12.6Limit Theorems
  1234. 12.6.1 The Law of Large Numbers
  1235. proof
  1236. proof
  1237. Solution
  1238. Solution
  1239. Solution
  1240. 12.6.2 The Central Limit Theorem
  1241. Solution
  1242. Solution
  1243. Solution
  1244. Solution
  1245. Estimating Sample Sizes
  1246. Solution
  1247. Section12.6 Problems
  1248. 12.6.1
  1249. 12.6.2
  1250. Cystic Fibrosis
  1251. 12.7 Statistical Tools
  1252. 12.7.1 Describing Univariate Data
  1253. Solution
  1254. Solution
  1255. Solution
  1256. 12.7.2 Estimating Parameters
  1257. Point Estimates of Means
  1258. Solution
  1259. A Remark on Using the Sample Mean to Estimate the Mean
  1260. Point Estimates of Proportions
  1261. Solution
  1262. Solution
  1263. Point Estimates of Variances
  1264. Solution
  1265. Confidence Intervals
  1266. Solution
  1267. Solution
  1268. Solution
  1269. Interpreting Mean±S.E.
  1270. Solution
  1271. 12.7.3 Linear Regression
  1272. Solution
  1273. Solution
  1274. Section12.7 Problems
  1275. 12.7.1
  1276. 12.7.2
  1277. 12.7.3
  1278. Chapter 1 Review
  1279. Key Terms
  1280. Review Problems
  1281. Appendices
  1282. Answers to Odd-Numbered Problems
  1283. Section 1.1 (Includes Even-Numbered Problems)
  1284. Section 1.2
  1285. Section 1.3
  1286. Section 1.4
  1287. Chapter 1 Review Problems
  1288. Section 2.1
  1289. Section 2.2
  1290. Section 2.3
  1291. Chapter 2 Review Problems
  1292. Section 3.1
  1293. Section 3.2
  1294. Section 3.3
  1295. Section 3.4
  1296. Section 3.5
  1297. Section 3.6
  1298. Chapter 3 Review Problems
  1299. Section 4.1
  1300. Section 4.2
  1301. Section 4.3
  1302. Section 4.4
  1303. Section 4.5
  1304. Section 4.6
  1305. Section 4.7
  1306. Section 4.8
  1307. Section 4.9
  1308. Section 4.10
  1309. Section 4.11
  1310. Chapter 4 Review Problems
  1311. Section 5.1
  1312. Section 5.2
  1313. Section 5.3
  1314. Section 5.4
  1315. Section 5.5
  1316. Section 5.6
  1317. Section 5.7
  1318. Section 5.8
  1319. Section 5.9
  1320. Section 5.10
  1321. Chapter 5 Review Problems
  1322. Section 6.1
  1323. Section 6.2
  1324. Section 6.3
  1325. Chapter 6 Review Problems
  1326. Section 7.1
  1327. Section 7.2
  1328. Section 7.3
  1329. Section 7.4
  1330. Section 7.5
  1331. Section 7.6
  1332. Section 7.7
  1333. Chapter 7 ReviewProblems
  1334. Section 8.1
  1335. Section 8.2
  1336. Section 8.3
  1337. Section 8.4
  1338. Chapter 8 Review Problems
  1339. Section 9.1
  1340. Section 9.2
  1341. Section 9.3
  1342. Section 9.4
  1343. Section 9.5
  1344. Chapter 9 Review Problems
  1345. Section 10.1
  1346. Section 10.2
  1347. Section 10.3
  1348. Section 10.4
  1349. Section 10.5
  1350. Section 10.6
  1351. Section 10.7
  1352. Section 10.8
  1353. Section 10.9
  1354. Chapter 10 Review Problems
  1355. Section 11.1
  1356. Section 11.2
  1357. Section 11.3
  1358. Section 11.4
  1359. Section 11.5
  1360. Chapter 11 Review Problems
  1361. Section 12.1
  1362. Section 12.2
  1363. Section 12.3
  1364. Section 12.4
  1365. Section 12.5
  1366. Section 12.6
  1367. Section 12.7
  1368. Chapter 12 Review Problems
  1369. References
  1370. Index
  1371. A
  1372. B
  1373. C
  1374. D
  1375. E
  1376. F
  1377. G
  1378. H
  1379. I
  1380. J
  1381. K
  1382. L
  1383. M
  1384. N
  1385. O
  1386. P
  1387. Q
  1388. R
  1389. S
  1390. T
  1391. U
  1392. V
  1393. W
  1394. Y
  1395. Z

 

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