Math 2
Calculus with Algebra and Trigonometry
Last updated February 6, 2004

 General Information Syllabus Homework

### Homework

Problem Set 0
(Due Monday, January 12)
 Chapter 1: Functions Section 1: Functions and Growth. problems 11, 17 Section 2: New Functions from Old. problems 2, 12, 13 Section 3: Families of Functions and Modeling. problem 2 Section 4: Introduction to Continuity. problems 1, 2, 6 Chapter 2: Derivatives Section 1: How do we Measure Speed? problems 1, 3 Section 2: The Derivative at a Point. problems 12, 19 Section 3: The Derivative Function. problems 6, 13 Chapter 3: Shortcuts to Differentiation Section 1: Powers and Polynomials. problems 17, 20, 35 Section 2: The Exponential Function. problems 1, 18 Section 3: The Product and Quotient Rules. problems 10, 16 Section 4: The Chain Rule. problems 1, 11, 21 Section 5: The Trigonometric Functions. problems 3, 12 Section 6: Applications of the Chain Rule. problems 12, 34

Problem Set 1
(Due Thursday, January 15)
 Position, Velocity, Acceleration: Read: section 2.5 Goals: Understand the relationship between position, velocity, and acceleration in terms of first and second derivatives; solve problems of motion using these concepts; interpret real-world statements in terms of derivatives. Required Problems: p.77 11, 13. p.80: 20. Recommended Problems: p.77: 15, 16, 18. Curve Sketching: Read: section 4.1 Goals: Define local maximum, local minimum, critical point, inflection point; identify these types of points using first and second derivative tests; sketch curves (including local maxima and minima, inflection points, concavity, and asymptotic behavior). Required Problems: p.161: 4, 17, 22. Recommended Problems: p.161: 7. p.196: 7, 8, 11, 12, 13.

Writing Assignment 1
(Due Wednesday, January 21)
 The Motorcycle Dude Summary: Help Evyl K. determine the correct time at which to accelerate so that he can catch the cash and ride off into the sunset. Assignment text         Grading checklist         Writing in Mathematics Guide

Problem Set 2
(Due Friday, January 23)
 Optimization: Read: sections 4.3, 4.5 Goals: Understand the difference between local and global maxima and minima; be able to mathematically model a problem (translate a word problem into a function); use derivatives to optimize a function. Required Problems: p.173: 9. p.189: 4, 7. Bonus: p.189: 17. Recommended Problems: p.173: 1, 2, 13, 16. p.189: 5, 6, 8, 13--15. Related Rates: Read: section 3.6 Goals: Recognize related rates problems and how the chain rule applies. Required Problems: p.147: 18. Recommended Problems: p.135: 33, 34. p.147: 17, 19. Marginality: Read: section 4.4 Goals: Determine qualitative information from the graphs of cost and revenue functions; sketch cost and revenue functions given qualitative information; understand marginal cost and marginal revenue as derivatives; maximize profit given total cost and revenue functions. Required Problems: p.182: 3, 5. Recommended Problems: p.182: 10.

Problem Set 3
(Due Thursday, January 29)
 Theorems of Differential Calculus; Riemann Sums: Read: end of chapter 4 (pp.201--207), section 5.1 Goals: Recognize and understand the Extreme Value Theorem, Mean Value Theorem, Constant Function Theorem, and the Racetrack Principle; be able to apply these theorems to explain facts about abstract and particular functions; understand relationship between distance traveled and area under velocity graph; use Riemann sums to approximate area. Required Problems: p.205: 1, 9. p.215: 2. Recommended Problems: p.205: 18. p.215: 1, 5, 9. Limits of Riemann Sums; Definite Integrals; Rules for Integrals: Read: sections 5.2, 5.4 Goals: Understand how a limit of Riemann sums yields the exact area under a curve; understand integral notation; interpret integrals as area; be able to estimate integrals; use rules for integrals (sums, multiples, limits of integration). Required Problems: p.222: 13, 24. p.237: 14. Recommended Problems: p.222: 2, 10, 13, 15, 23, 25. p.237: 2, 15--19, 20, 21, 23, 24. p.240: 10.

Writing Assignment 2
(Due Wednesday, February 4)
 Over the River Summary: Minimize the cost of laying electric cable across the river to Mr. Beegshoat's summer cabin. Assignment text         Grading checklist         Writing in Mathematics Guide

Problem Set 4
(Due Thursday, February 5)
 The Fundamental Theorem of Calculus: Read: sections 5.4, 6.4 Goals: Create area functions using integrals; understand the derivative of area functions; understand relationship between total change of a function, integrating the derivative of that function, and how this yields a method to evaluate integrals exactly. Required Problems: Write down the Fundamental Theorem of Calculus Recommended Problems: Memorize the Fundamental Theorem of Calculus Antiderivatives: Read: section 6.1 Goals: Understand the relationship between values of a function at a point and the slope of an antiderivative function at that point; given the graph of a function, sketch the graph of an antiderivative of that function. Required Problems: p.257: 1. Recommended Problems: p.257: 2--7. Antiderivatives: Read: sections 6.2 Goals: Learn and use the formulas for antiderivatives of xn, 1/x, ex, sin(x), cos(x); understand the difference between definite and indefinite integrals; explicitly calculate definite integrals using the Fundamental Theorem of Calculus. Required Problems: p.262: 15, 56. Recommended Problems: p.262: 1--14, 16--18, 30--41, 57, 58.

Problem Set 5
(Due Thursday, February 12)
 Differential Equations: Read: section 6.3, section 10.4 Goals: Recognize and solve differential equations; correctly apply seperation of variables when necessary; use initial conditions to determine values for constants that arise while antidifferentiating; understand how a distance function may be derived given a constant acceleration; solve population growth / exponential decay / compounded interest problems posed as differential equations. Required Problems: p.267: 14. p.471: 1. Recommended Problems: p.267: 1, 3, 6, 11, 21. p.471: 2, 3, 4, 5, 6. Substitution: Read: section 7.1 Goals: Understand analogy to the chain rule from differential calculus; recognize when substitution may simplify and aid solving an indefinite integral; choose likely candidates for the "inside function"; use substitution to reduce a problem to an easier one. Required Problems: p.286: 6, 25. Recommended Problems: p.286: 4, 30, 39, 43. Substitution: Read: section 7.2 Goals: Solve definite integral problems which may require a substitution; understand two methods for handling bounds of integration when substituting. Required Problems: p.291: 7, 29. Recommended Problems: p.291: 2, 17, 26.

Writing Assignment 3
(Due Wednesday, February 18)
 Blowing up Balloons Summary: At what rate can Mr. Mekkstosi inflate balloons so that they do not explode? Assignment text         Grading checklist         Writing in Mathematics Guide

Problem Set 6
(Due Thursday, February 19)
 Integration by Parts: Read: section 7.3 Goals: Understand analogy to the product rule from differential calculus; recognize when integration by parts may simplify and aid solving an indefinite integral; solve definite and indefinite integral problems requiring integration by parts. Required Problems: p.297: 5, 10, 15, 39, 47. Recommended Problems: p.297: 2, 19, 23, 33.

Problem Set 7
(Due Friday, February 27)
 Using Integral Tables: Read: section 7.4 Goals: Use formulas from integral tables; use substitution to transform an integral to a form found in integral tables; understand how completing the square, partial fractions, and trigonometric substitutions are used in integral tables. Required Problems: p.303: 2, 9. Recommended Problems: p.303: 4, 7, 15, 23, 37. Improper Integrals: Read: section 7.7 Goals: Define convergent and divergent integrals; rewrite and solve integrals with infinite bounds using limits; integrate over intervals where functions have vertical asymptotes; checking for convergence using comparisions. Required Problems: p.323: 4, 11. Recommended Problems: p.323: 1--3, 5--10, 12--15. Volumes: Read: section 8.1 Goals: Visualize solids of revolution (generated by revolving curves around the x-axis); determine volumes of such solids; use integrals to determine arclengths of functions; use integrals to determine surface areas of solids of revolution. Required Problems: p.344: 7, 16. Recommended Problems: p.344: 2, 3, 5, 8.

Writing Assignment 4
(Due Wednesday, March 4)
 Counting Bacteria Summary: Help Cimondo save his biology experiment by determining a bacteria population. Assignment text         Grading checklist         Writing in Mathematics Guide