 ## Math 119 Calculus With Analytic Geometry (Summer 2015)

#### This page is for archival purposes only! Students should use ODTU-Class

There will be 28 lectures given by the instructors, each lasting 2 class hours. The actual timing of the lectures will differ slightly from section to section because of the holidays, but the total number will be the same. Besides these lectures, there will be recitations, 2 hours per week, during which the assistants will solve extra problems and give quizzes.

The table below is a rough guideline for the content of course lectures. Professors may reorder content as necessary/desired. The section and page numbers below are from the textbook, Calculus, by James Stewart, 7th international metric ed., 2012.

Exam dates will be determined by the administration and are currently only approximate guesses.

 Week 1: Jun.29-Jul.3 1 Chapter 1. Functions and Limits§1.4: The Tangent and Velocity Problems. §1.5: The Limit of a Function. 2 §1.6: Calculating Limits Using the Limit Laws. §1.8: Continuity. 3 §1.7: The Precise Definition of a Limit. 4 Chapter 2. Derivatives§2.1: Derivatives and Rates of Change. §2.2: The Derivative as a Function. 5 §2.3: Differentiation Formulas. §2.4: Derivatives of Trigonometric Functions. Week 2: Jul.6-10 6 §2.5: The Chain Rule. §2.6: Implicit Differentiation. 7 §2.8: Related Rates. 8 §2.9: Linear Approximations and Differentials. Chapter 3. Applications of Differentiation§3.1: Maximum and Minimum Values. 9 §3.2: The Mean Value Theorem. §3.3: How Derivatives Affect the Shape of a Graph. Week 3: Jul.13-17 10 §3.4: Limits at Infinity; Horizontal Asymptotes. 11 §3.5: Summary of Curve Sketching. 12 §3.7: Optimization Problems. 13 §3.8: Newton's Method (Reading Assignment). §3.9: Antiderivatives. 14 Chapter 4. Integrals§4.1: Areas and Distances. §4.2: The Definite Integral. Week 4: Jul.20-24 15 §4.3: The Fundamental Theorem of Calculus. §4.4: Indefinite Integrals and the Net Change Theorem. 16 §4.5: The Substitution Rule. Chapter 5. Applications of Integration§5.1: Areas between Curves. §5.5: Average Value of a Function. 17 §5.2: Volumes (Disks). §5.3: Volumes by Cylindrical Shells. 18 Chapter 6. Inverse Functions; Exp, log, and trig§6.1: Inverse Functions. §6.2: Exponential Functions and Their Derivatives. §6.2*: The Natural Logarithmic Function. Week 5: Jul.27-31 19 §6.3: Logarithmic Functions. §6.3*: The Natural Exponential Function. §6.4: Derivatives of Logarithmic Functions. §6.4*: General Logarithmic and Exponential Functions. 20 §6.6: Inverse Trigonometric Functions. §6.7: Hyperbolic Functions (Reading Assignment). §6.8: Indeterminate Forms and L'Hospital's rule. 21 Chapter 7. Techniques of Integration§7.1: Integration by Parts. 22 §7.2: Trigonometric Integrals. 23 §7.3: Trigonometric Substitution. Week 6: Aug.3-7 24 §7.4.1: Integration of Rational Functions by Partial Fractions (I, II). 25 §7.4.2: Integration of Rational Functions by Partial Fractions (III, IV). §7.5: Strategy for Integration. 26 §7.7: Approximate Integration. §7.8: Improper Integrals. 27 Chapter 8. Further Applications of Integration§8.1: Arc Length. Week 7: Aug.10-11 28 §8.2: Area of a Surface of Revolution. FINAL EXAM