Content

• Numbers and functions
• Limits and continuity of functions of one variable
• Differentiability of functions of one variable: interpretations, calculation rules, higher order derivatives, differentials, maxima and minima, monotonicity and concavity, implicit differentiation, practical problems, graphing functions
• Introduction to differential equations: first-order separable differential equations
• Integration theory and integration methods: fundamental theorems, simple integrals, applications: area, volume and length, integration techniques
• Transcendental functions: inverse functions, logarithmic and exponential functions, inverse trigonometric functions, hyperbolic functions, exponential growth and decay
• Limits: indeterminate forms, L'Hospital's rule
• Limits and continuity of multivariate functions
• Differentiability of multivariate functions: partial derivatives, directional derivatives, gradient, the chain rule, maxima and minima, the method of Lagrange multipliers

Course material

Handbook: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon: Calculus, ninth edition, Pearson International Edition (or a later edition)

Other calculus handbooks can be useful as well.

Format: more information

For each (weekly) session the students prepare (part of) a chapter and make a list of exercises. The session consists of discussion and questions about theory and exercises.

Off-campus students can ask questions during online sessions.