Honors Calculus I: Math 1181H Section 0110 - Autumn 2018

Handouts

• Calendar
• Syllabus
• Generic course info

Textbook

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

Exams

• Midterm 1: Monday, September 17, 2018 (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 19, 2018 (in class). Topics: Chapters 5-9. Practice midterm 2, Solutions for practice midterm 2, Solutions for midterm 2.
• Midterm 3: Tuesday, November 20, 2018 (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 10, 2018, 10:00am-11:45am (location: JR 304 (usual lecture room)).

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.

• Quiz 1: Friday, September 7, 2018 (in class). Solutions.
• Quiz 2: Thursday, October 15, 2018 (in class). Solutions.
• Quiz 3: Friday, November 16, 2018 (in class). Solutions.
• Quiz 4: Tuesday, December 5th, 2018 (in class) Solutions.

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 27)
• Homework 2: Sections 2.6, 3.1, 3.2, 3.3, 3.4 and 3.5 (due date: Sept. 6)
• Homework 3: Sections 3.6, 4.1, 4.2, 4.3, 4.4 and 4.5 (due date: Sept. 13) [Problem 28 (sect. 4.3)] [Problem 16 (sect. 4.5)]
• Homework 4: Sections 5.2, 5.3, 5.4 and 5.5 (due date: Sept. 24)
• Homework 5: Sections 6.3, 6.5, 6.6 and 6.7 (due date: Oct. 1)
• Homework 6: Sections 7.2, 7.3, 7.4, 7.5, and 7.6 (due date: Oct. 5) [Problem 9 (Section 7.6)]
• Homework 7: Sections 7.7, 8.2, 8.3, 8.4 and 8.5 (due date: Oct. 10)
• Homework 8: Sections 9.1, 9.2, 9.3, 9.4, 9.5 and 9.6 (due date: Oct. 17)
• Homework 9: Sections 10.2, 10.3, 10.4, 10.5 and 10.6 (due date: Oct. 26)
• Homework 10: Sections 10.7, 10.8, 12.2, 12.3 and 12.4 (due date: Nov. 2)
• Homework 11: Sections 13.2, 13.3 and 13.4 (due date: Nov. 9)
• Homework 12: Sections 13.5, 13.6, 13.7 and 13.8 (due date: Nov. 16)
• Homework 13: Sections 14.2, 14.3 and 14.4 (new due date: Nov. 30)
• 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 21, 2018.
• Lecture 2 (§ 2.2 (cont.): "How to calculate the slope of a tangent.", and § 2.3: "The definition of the derivative."), August 22, 2018.
• Lecture 3 (§ 2.5: "The concept of a limit."), August 23, 2018.
• Lecture 4 (§ 2.5 (cont.): "Two trigonometric limits.", and § 2.4: "Velocity and rates of change. Newton and Leibniz."), August 24, 2018.
• Week 2:
• Lecture 5 (§ A2: "Theorems about limits. Uniqueness of limits and Squeeze Theorem"), August 27, 2018.
• Lecture 6 (§ A2: "Limit laws," and § 2.6: "Continuous functions. The Intermediate Value Theorem."), August 28, 2018.
• Lecture 7 (§ 2.6 (cont.): "The Mean Value Theorem and the Extreme Values Theorem."), August 29, 2018.
• Lecture 8 (§ 3.1: "Derivatives of polynomials.", and § 3.2: "The product and quotient rules."), August 30, 2018.
• Lecture 9 (§ 3.3: "Composite functions and the Chain Rule."), August 31, 2018.
• Week 3:
• Lecture 10 (§ 3.4: "Some trigonometric derivatives."), September 4, 2018.
• Lecture 11 (§ 3.5: "Implicit functions an Fractional exponents."), September 5, 2018.
• Lecture 12 (§ 3.6: "Derivatives of higher order.", and § A4: "The Mean Value Theorem."), September 6, 2018.
• Lecture 13 (§ 4.1: "Increasing and decreasing functions. Maxima and Minima."), September 7, 2018.
• Week 4:
• Lecture 14 (§ 4.2: "Concavity and points of inflection."), September 10, 2018.
• Lecture 15 (§ 4.3: "Applied maximum and minimum problems.", and § 4.4: "More Maximum-Minimum problems."), September 11, 2018.
• Lecture 16 (§ 4.4 (cont.): "More Maximum-Minimum problems.", and § 4.5: "Related rates."), September 12, 2018.
• Lecture 17 (§ 4.4 (cont.): "Reflection and refraction." ), September 13, 2018.
• Week 5:
• Lecture 18 (§ 5.1: "Introduction.", and § 5.2: "Differentials and tange line approximations."), September 18, 2018.
• Lecture 19 (§ 5.3: "Indefinite integrals. Integration by substitution." and § 5.4: "Differential equations. Separation of variables."), September 19, 2018.
• Lecture 20 (§ 5.5: "Motion under Gravity. Escape velocity and black holes."), September 20, 2018.
• Lecture 21 (§ 6.1: "Introduction.", and § 6.2: "The problem of areas."), September 21, 2018.
• Week 6:
• Lecture 22 (§ 6.3: "The Sigma notation and certain special sums.", and § 6.4: "The area under a curve. Definite integrals. Riemann sums."), September 25, 2018.
• Lecture 23 (§ 6.5: "The computation of areas as limits." and § 6.7: "Properties of definite integrals."), September 26, 2018.
• Lecture 24 (§ 6.7 (cont.): "Algebraic vs Geometric areas.", and § 6.6: "The Fundamental Theorem of Calculus."), September 27, 2018.
• Lecture 25 ( § 7.1: "Introduction. The intuitive meaning of integration.", and § 7.2: "The area between two curves."), September 28, 2018.
• Week 7:
• Lecture 26 (§ 7.2 (cont.): "The area between two curves." and § 7.3: "Volumes: The disk method."), October 1, 2018.
• Lecture 27 (§ 7.3: "Volumes via moving slices", and § 7.4: "Volumes: The method of cylindrical shells."), October 2, 2018. [Visualization aid for cylindrical shells: nested cups]
• Lecture 28 (§ 7.5: "Arc length.", and § 7.6: "The area of a surface of revolution."), October 3, 2018.
• Lecture 29 (§ 7.7: "Work and energy."), October 4 and 5, 2018.
• Week 8:
• Lecture 30 (§ 8.2: "Review of exponents and Logarithms.", § 8.3: "The number e and the function y=e^x"), and § 8.4: "The natural logarithm function y=ln x."), October 5, 2018.
• Lecture 31 (§ 8.4 (cont.): "The natural logarithm function y=ln x.", and § 8.5: "Applications. Popularity growth and radioactive decay."), October 8, 2018.
• 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 9, 2018.
• Week 9:
• Lecture 33 (§ 9.5: "The inverse trigonometric functions."), October 15, 2018.
• Lecture 34 (§ 9.6: "Simple harmonic motion. The Pendulum."), October 16 and 17, 2018.
• Week 10:
• Lecture 35 (§ 10.1: "Introduction. The basic formulas.", § 10.2: "The method of substitution.", and § 10.3: "Certain trigonometric integrals."), October 22, 2018.
• Lecture 36 (§ 10.4: "Trigonometric substitutions.", § 10.5: "Completing the square."), October 23, 2018. [Tractrix curve in action]
• Lecture 37 (§ 10.6: "The method of partial fractions." ), October 24, 2018.
• Lecture 38 (§ 10.7: "Integration by parts." and § 10.8: "A mixed bag. Strategy for dealing with Integrals of miscellaneous types."), October 25, 2018.
• Lecture 39 (§ 12.1: "Introduction.", and § 12.2: "The indeterminate form 0/0. L'Hospital's Rule."), October 26, 2018.
• Week 11:
• Lecture 40 (§ 12.1 (cont.): "The Mean Value Theorem revisited.", and § 12.3: "Other indeterminate forms."), October 29, 2018.
• Lecture 41 (§ 12.3 (cont.): "Other indeterminate forms.", and § 12.4: "Improper integrals."), October 30, 2018.
• Lecture 42 (§ 13.1: "What is an infinite series?"), October 31, 2018.
• Lecture 43 (§ 13.2: "Convergent sequences."), November 1, 2018.
• Lecture 44 (§ 13.2 (cont.): "Convergent sequences.""), November 2, 2018.
• Week 12:
• Lecture 45 (§ 13.3: "Convergent and divergent series.), November 5, 2018.
• Lecture 46 (§ 13.3: "Convergent and divergent series.", and § 13.4: "General properties of convergent series." ), November 6, 2018.
• Lecture 47 (§ 13.4 (cont.): "General properties of convergent series.", and § 13.6: "The integral test."), November 7, 2018.
• Lecture 48 (§ 13.6 (cont.): "The integral test. Euler's constant.", and § 13.7: "The ratio test and root test."), November 8, 2018.
• Lecture 49 (§ 13.5: "Series of nonnegative terms. Comparison tests."), November 9, 2018.
• Week 13:
• Lecture 50 (§ 13.5 (cont.): "Series of nonnegative terms. Comparison tests.", and § 13.7 (cont.): "The ratio test and root test."), November 13, 2018.
• Lecture 51 (§ 13.8: "The alternating series test. Absolute convergence."), November 14, 2018.
• Lecture 52 (Appendix A13: "Absolute vs. conditional convergence."), November 15, 2018.
• Lecture 53 (§ 14.1: "Introduction.", and § 14.2: "The interval of convergence."), November 16, 2018.
• Week 15:
• Lecture 54 (§ 14.2 (cont.): "The interval of convergence."), November 26, 2018.
• Lecture 55 (§ 14.3: "Differentiation and integration of power series." and § 14.4: "Taylor series and Taylor's formula."), November 27 and 28, 2018.
• Lecture 56 (§ 14.4 (cont.): "Taylor series and Taylor's formula."), November 29, 2018.
• Lecture 57 (§ 14.5: "Computations using Taylor's formula.", § 14.6: "Applications to Differential Equations."), November 30, 2018.
• Week 16:
• Lecture 58 (§ 14.7: "Operations on Power series." and § A16: "Division of power series."), December 3, 2018.
• Lecture 59 (§ 14.3 (cont.): "Differentiation and integration of power series." and § A15: "Uniform convergence for power series."), December 4, 2018.

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