### Handouts

### Textbook

**Title:**Calculus with Analytic Geometry**Edition:**2nd.**Author:**Simmons**Publisher:**McGraw Hill**ISBN:**9780070576424

### Exams

**Midterm 1:**Tuesday, September 19, 2017 (in class).**Topics:**Chapters 2-4; Appendices A2 and A4. Practice midterm 1, Solutions for practice midterm 1, Solutions for midterm 1.**Midterm 2:**Friday, October 20, 2017 (in class).**Topics:**Chapters 5-9. Practice midterm 2, Solutions for practice midterm 2, Solutions for midterm 2.**Midterm 3:**Tuesday, November 21, 2017 (in class).**Topics:**Chapters 10, 12, and 13. - Practice midterm 3 , Solutions for practice midterm 3, Solutions for midterm 3.**Final exam**(__CUMULATIVE__): Monday, December 11, 2017, 10:00am-11:45am (location: CH 232) Practice final .

### Quizzes

Four quizzes will be given at random and will consist of problems very similar to those on the homework. The quizzes will be worth 5 points each. No make-up quizzes will be allowed, but the**lowest score**will be dropped.

### Homeworks

The homework problems are designed to understand the material discussed during the lectures and they will be assigned on each lecture. You are encourage to solve these problems the same day. Links to the homework assigments (in pdf formal) will be uploaded the day before the homework is due.There will a total of 14 homeworks, and only some of the problems from each set are required to be turned in. Each homework set will be worth 12 points. No late homework will be accepted, but the

**two lowest scores**will be dropped.

**Homework 1:**Sections 2.2, 2.3, 2.4 and 2.5 (due date: Aug 28)**Homework 2:**Sections 2.6, 3.1, 3.2 and 3.3 (due date: Sept. 5)**Homework 3:**Sections 3.4, 3.5, 3.6, 4.1, 4.2, 4.3, 4.4 and 4.5 (due date: Sept. 14)**Homework 4:**Sections 5.2, 5.3, 5.4 and 5.5 (due date: Sept. 22)**Homework 5:**Sections 6.3, 6.5, 6.6 and 6.7 (due date: Sept. 28)**Homework 6:**Sections 7.2, 7.3, 7.4, 7.5, 7.6 and 7.7 (due date: Oct. 6) [Problem 8 in Section 7.6]**Homework 7:**Sections 8.2, 8.3, 8.4 and 8.5 (due date: Oct. 11)**Homework 8:**Sections 9.1, 9.2, 9.3, 9.4, 9.5 and 9.6 (due date: Oct. 18)**Homework 9:**Sections 10.2, 10.3, 10.4, 10.5 and 10.6 (due date: Oct. 26)**Homework 10:**Sections 10.7, 12.2, 12.3 and 12.4 (due date: Nov. 2)**Homework 11:**Sections 13.2, 13.3 and 13.4 (due date: Nov. 8)**Homework 12:**Sections 13.5, 13.6, 13.7 and 13.8 (due date: Nov. 15)**Homework 13:**Sections 14.2, 14.3 and 14.4 (due date: Nov. 29)**Homework 14:**Sections 14.5, 14.6, 14.7 and 14.8 (due date: Dec. 4)

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### Lectures

**Week 1:**- Lecture 1 (§ 2.1: "What is Calculus? The problem of tangents.", and § 2.2: "How to calculate the slope of a tangent."), August 22, 2017.
- Lecture 2 (§ 2.2 (cont.): "How to calculate the slope of a tangent.", and § 2.3: "The definition of the derivative."), August 23, 2017.
- Lecture 3 (§ 2.5: "The concept of a limit."), August 24, 2017.
- Lecture 4 (§ 2.5 (cont.): "Two trigonometric limits.", and § 2.4: "Velocity and rates of change. Newton and Leibniz."), August 23, 2017.
**Week 2:**- Lecture 5 (§ A2: "Theorems about limits."), August 28, 2017.
- Lecture 6 (§ 2.6: "Continuous functions. The Mean Value Theorem and the Intermediate Value Theorem."), August 29, 2017.
- Lecture 7 (§ 2.6 (cont.): "The Extreme Values Theorem.", and § 3.1: "Derivatives of polynomials."), August 30, 2017.
- Lecture 8 (§ 3.2: "The product and quotient rules."), August 31, 2017.
- Lecture 9 (§ 3.3: "Composite functions and the Chain Rule."), September 1, 2017.
**Week 3:**- Lecture 10 (§ 3.4: "Some trigonometric derivatives."), September 5, 2017.
- Lecture 11 (§ 3.5: "Implicit functions an Fractional exponents."), September 6, 2017.
- Lecture 12 (§ 3.6: "Derivatives of higher order.", and § A4: "The Mean Value Theorem."), September 7, 2017.
- Lecture 13 (Appendix A3: "The Extreme Value Theorem." and § 4.1: "Increasing and decreasing functions. Maxima and Minima."), September 8, 2017.
**Week 4:**- Lecture 14 (§ 4.2: "Concavity and points of inflection."), September 11, 2017.
- Lecture 15 (§ 4.3: "Applied maximum and minimum problems.", and § 4.4: "More Maximum-Minimum problems."), September 12, 2017.
- Lecture 16 (§ 4.5: "Related rates."), September 13, 2017.
- Lecture 17 (§ 5.1: "Introduction.", and § 5.2: "Differentials and tange line approximations."), September 14, 2017.
- Lecture 18 (§ 5.3: "Indefinite integrals. Integration by substitution."), September 15, 2017.
**Week 5:**- Lecture 19 (§ 5.4: "Differential equations. Separation of variables.", and § 5.5: "Motion under Gravity. Escape velocity and black holes."), September 20 and 21, 2017.
- Lecture 20 (§ 6.1: "Introduction.", § 6.2: "The problem of areas.", and § 6.3: "The Sigma notation and certain special sums."), September 22, 2017.
**Week 6:**- Lecture 21 (§ 6.4: "The area under a curve. Definite integrals. Riemann.", and § 6.5: "The computation of areas as limits."), September 25, 2017.
- Lecture 22 (§ 6.7: "Properties of definite integrals.", and § 6.6: "The Fundamental Theorem of Calculus."), September 26, 2017.
- Lecture 23 (§ 7.1: "Introduction. The intuitive meaning of integration.", and § 7.2: "The area between two curves."), September 27, 2017.
- Lecture 24 (§ 7.3: "Volumes: The disk method."), September 28, 2017.
- Lecture 25 (§ 7.4: "Volumes: The method of cylindrical shells."), September 29, 2017.
**Week 7:**- Lecture 26 (§ 7.5: "Arc length."), October 2, 2017.
- Lecture 27 (§ 7.6: "The area of a surface of revolution."), October 3, 2017.
- Lecture 28 (§ 7.7: "Work and energy."), October 4, 2017.
- Lecture 29 (§ 8.2: "Review of exponents and Logarithms."), October 5, 2017.
- Lecture 30 (§ 8.3: "The number
*e*and the function*y=e*", Appendix A7: "The existence of e = lim^{x}_{h→0}(1 + h)^{1/h}.", and § 8.4: "The natural logarithm function*y=ln x*. Euler."), October 6, 2017. **Week 8:**- Lecture 31 (§ 8.4 (cont.): "The natural logarithm function
*y=ln x*. Euler.", and § 8.5: "Applications. Popularity growth and radioactive decay."), October 9, 2017. - Lecture 32 (§ 9.1: "Review of Trigonometry.", § 9.2: "The derivatives of the sine and cosine.", § 9.3: "The integrals of the sine and cosine. The Needle problem.", and § 9.4: "The derivatives of the other four functions."), October 10, 2017.
- Lecture 33 (§ 9.5: "The inverse trigonometric functions."), October 11, 2017.
**Week 9:**- Lecture 34 (§ 9.6: "Simple harmonic motion. The Pendulum."), October 16 and 17, 2017.
- Lecture 35 (§ 10.1: "Introduction. The basic formulas.", § 10.2: "The method of substitution.", and § 10.3: "Certain trigonometric integrals."), October 18, 2017.
**Week 10:**- Lecture 36 (§ 10.4: "Trigonometric substitutions.", § 10.5: "Completing the square."), October 23, 2017.
- Lecture 37 (§ 10.6: "The method of partial fractions.", and § 10.7: "Integration by parts." ), October 24, 2017.
- Lecture 38 (§ 10.8: "A mixed bag. Strategy for dealing with Integrals of miscellaneous types."), October 25, 2017.
- Lecture 39 (§ 12.1: "Introduction. The Mean Value Theorem revisited.", and § 12.2: "The indeterminate form 0/0. L'Hospital's Rule."), October 26, 2017.
- Lecture 40 (§ 12.3: "Other indeterminate forms."), October 27, 2017.
**Week 11:**- Lecture 41 (§ 12.4: "Improper integrals."), October 30, 2017.
- Lecture 42 (§ 13.1: "What is an infinite series?"), October 31, 2017.
- Lecture 43 (§ 13.2: "Convergent sequences."), November 1, 2017.
- Lecture 44 (§ 13.2 (cont.): "Convergent sequences.", § 13.3: "Convergent and divergent series."), November 2 and November 3, 2017.
**Week 12:**- Lecture 45 (§ 13.3 (cont.): "Convergent and divergent series.", and § 13.4: "General properties of convergent series."), November 6, 2017.
- Lecture 46 (Appendix A7: "The existence of e = lim
_{h→0}(1 + h)^{1/h}."), November 7, 2017. - Lecture 47 (§ 13.5: "Series of nonnegative terms. Comparison tests."), November 8, 2017.
- Lecture 48 (§ 13.6: "The integral test. Euler's constant."), November 9, 2017.
**Week 13:**- Lecture 49 (§ 13.7: "The ratio test and root test."), November 13, 2017.
- Lecture 50 (§ 13.8: "The alternating series test. Absolute convergence."), November 14, 2017.
- Lecture 51 (§ A13: "Absolute vs. conditional convergence."), November 15, 2017.
- Lecture 52 (§ 14.1: "Introduction.", and § 14.2: "The interval of convergence."), November 16, 2017.
- Lecture 53 (§ 14.2 (cont.): "The interval of convergence.", and § 14.3: "Differentiation and integration of power series."), November 17, 2017.
**Week 15:**- Lecture 54 (§ 14.3 (cont.): "Differentiation and integration of power series.", and § 14.4: "Taylor series and Taylor's formula."), November 27, 2017.
- Lecture 55 (§ 14.4 (cont.): "Taylor series and Taylor's formula."), November 28, 2017.
- Lecture 56 (§ 14.5: "Computations using Taylor's formula."), November 29, 2017.
- Lecture 57 (§ A15: "Uniform convergence for power series.", and § 14.6: "Applications to Differential Equations."), November 30, 2017.
- Lecture 58 (§ 14.7: "Operations on Power series.", and § A16: "Division of power series."), December 1, 2017.

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