Calculus 30

Unit 1: Functions and Limits

Extending function analysis, factoring and inequalities, and the ideas of limit and continuity that underlie all of calculus.

• Classifying and analyzing functions
• Rational functions: asymptotes, holes, and end behaviour

• Extending factoring
• Solving rational, double, and absolute-value inequalities

• The meaning of a limit
• Evaluating limits
• Continuity and discontinuity

Unit 2: Differentiation

The derivative as a rate of change, the rules of differentiation, curve sketching, applications of derivatives, and derivatives of transcendental functions.

• The derivative from first principles
• Rules of differentiation
• Implicit differentiation, tangents, and notation

• First-derivative analysis
• Second-derivative analysis and sketching

• Optimization
• Rates of change and related rates

• Defining e and differentiating transcendental functions
• Sketching and applying transcendental derivatives

Unit 3: Integration

Indefinite and definite integration by sight and by substitution, the Fundamental Theorem of Calculus, and area under and between curves.

• Indefinite integrals by sight and substitution

• The FTC and definite integrals
• Area under and between curves