Introductory Calculus

模块目标

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

课程大纲

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

   学习结果 Evaluate a limit from a definition or a named theorem, and give a jump discontinuity.

   形成性检查 四选一检查

2. 02 Differentiation and applications 25h

   学习结果 Differentiate compositions and products, and solve a related-rates or optimisation stem with hypotheses.

   形成性检查 书面推导

3. 03 Integration and the fundamental theorem 25h

   学习结果 State FTC and compute an integral by substitution or parts with the matching boundary terms.

   形成性检查 书面推导

4. 04 Sequences of functions (light) 15h

   学习结果 Give a case where a pointwise limit of derivatives is not the derivative of the limit.

   形成性检查 反例

5. 05 Several variables: partial derivatives 25h

   学习结果 Compute a gradient and a directional derivative and say when equality of mixed partials is assumed.

   形成性检查 书面推导

6. 06 Multiple integrals (introduction) 20h

   学习结果 Evaluate an iterated integral on a simple region and change order only when the region allows it.

   形成性检查 书面推导

7. 07 Synthesis 20h

   学习结果 Solve a short problem that combines differentiation, integration, and a several-variable step, naming each licence.

   形成性检查 书面推导

学习结果

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

学科技能

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

可迁移技能

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