Introductory Calculus

Module aims

Compute correctly while naming the theorem that licenses each interchange or substitution.

Course outline

1. 01 Limits and continuity of functions of one variable 20h

   Learning result Evaluate a limit from a definition or a named theorem, and give a jump discontinuity.

   Formative check Four-option check

2. 02 Differentiation and applications 25h

   Learning result Differentiate compositions and products, and solve a related-rates or optimisation stem with hypotheses.

   Formative check Written derivation

3. 03 Integration and the fundamental theorem 25h

   Learning result State FTC and compute an integral by substitution or parts with the matching boundary terms.

   Formative check Written derivation

4. 04 Sequences of functions (light) 15h

   Learning result Give a case where a pointwise limit of derivatives is not the derivative of the limit.

   Formative check Counterexample

5. 05 Several variables: partial derivatives 25h

   Learning result Compute a gradient and a directional derivative and say when equality of mixed partials is assumed.

   Formative check Written derivation

6. 06 Multiple integrals (introduction) 20h

   Learning result Evaluate an iterated integral on a simple region and change order only when the region allows it.

   Formative check Written derivation

7. 07 Synthesis 20h

   Learning result Solve a short problem that combines differentiation, integration, and a several-variable step, naming each licence.

   Formative check Written derivation

Learning results

Differentiate and integrate standard classes of functions with justification, and compute a first several-variable example with an explicit domain.

Subject skills

Limits of functions, derivatives, FTC, substitutions, partial derivatives, iterated integrals.

Transferable skills

Track domains; refuse an interchange that the course has not justified.