M408C is the standard first-semester calculus course, directed at students in the natural sciences and engineering. The emphasis is on problem-solving, not the theory of analysis. Topics include algebraic, trigonometric, logarithmic, and exponential functions, their limits, continuity, derivatives, maxima and minima, integration, area under a curve, and volumes of revolution.
Date | Subject | Reading | Problem Set Due |
---|---|---|---|
January 14 | Introduction | ||
January 16 | Exponential | 1.4-1.5 | |
January 17 | p-set 0 (not graded) | ||
January 21 | Logarithms | 1.5 | |
January 23 | Limits | 2.1-2.2 | |
January 24 | p-set 1 | ||
January 28 | Limit Laws | 2.3 | |
January 30 | Continuity-Limit at Infinity | 2.5-2.6 | |
January 31 | p-set 2 | ||
February 4 | The Derivative of a Function | 2.7-2.8 | |
February 6 | Midterm 1 | ||
February 7 | p-set 3 | ||
February 11 | Derivatives of Polynomials and Product Rules | 3.1-3.2 | |
February 13 | Derivatives of Trigonometric Functions | 3.2-3.3 | |
February 14 | p-set 4 | ||
February 18 | The Chain Rule - Implicit Differentiation | 3.4-3.5 | |
February 20 | Derivatives of Logarithms | 3.5-3.6 | |
February 21 | p-set 5 | ||
February 25 | Exponential Growth and Decay | 3.8-3.9 | |
February 27 | Related Rates & Linear Approximation | 3.9-3.10 | |
February 28 | p-set 6 | ||
March 4 | Maximum and Minimum Values | 4.1, 4.3 | |
March 6 | Midterm 2 | ||
March 7 | p-set 7 | ||
March 11 | The Second Derivative Test and MVT | 4.2-4.3 | |
March 13 | Summary of Curve Sketching | 4.5 | |
March 14 | p-set 8 | ||
March 18-21 | Spring Break | ||
March 25 | L’Hospital’s Theorem | 4.4 | |
March 27 | Optimization Problems | 4.7 | |
March 28 | p-set 9 | ||
April 1 | Antiderivatives | 4.9 | |
April 3 | Midterm 3 | ||
April 4 | p-set 10 | ||
April 8 | Areas and the Definite Integral | 5.1 | |
April 10 | The Fundamental Theorem of Calculus | 5.2-5.3 | |
April 11 | p-set 11 | ||
April 15 | Net Change & The Substitution Rule | 5.4-5.5 | |
April 17 | Areas Between Curves and Volumes | 6.1-6.2 | |
April 18 | p-set 12 | ||
April 22 | Volumes of Revolution and Averages | 6.2, 6.5 | |
April 24 | Midterm 4 | ||
April 25 | p-set 13 | ||
May 5 | Final Exam |