Material

The material for midterm 1 consists of the material covered in the lectures up Taylor expansion (discussed in lecture on Feburary 8), including

• The ladder of functions, asymptotics at ∞, asymptotics at 0, asymptotics at a.
• Limits, one-sided limits, blow-up and limits in the extended sense, limits at infinity.
• The linear approximation and the definition of the derivative,
• Continuity: gluing functions and derivatives.
• Differentiation rules: linearity, product rule, quotient rule, chain rule. Partial derivatives.
• Differentiation table: exponentials, logarithms, trigonometric functions
• Exponential growth and decay: finding solutions to the equation y′ = ry.
• Applications of the chain rule: implicit diffeerentiation and related rates.
• Shape of the curve: increase/decrease, concavity and convexity.
• Taylor expansion: definition of the expansion, computing by repeated differentiation, reading off coefficients.

Structure

This midterm is about mastering the basic skills of this course.

• The exam will last 50 minutes and consist of 15 questions, which will be marked correct/incorrect based on the final answer only.
• Students are required to score at least 80% (12/15) to pass the course.
• There will be three retakes, the last of which will be a section of the final exam.

For practice problems use worksheets, as well as the CLP problem book and Schaum’s Outline of Theory and Problems of Differential and Integral Calculus .

Practicalities

The exam will take place during class on Thursday, February 15.