university of western cape 105 intermediate

MATHS 105

Free study notes for MATHS 105 (MATHS105) at university of western cape, one topic at a time, each with worked examples and a practice quiz.

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Course Syllabus

  1. Introduction to Fundamental Theorem of Calculus Part 1 (FTC 1)
  2. Continuity and Differentiability of Functions and Area Functions
  3. Applications of FTC 1: Differentiating Partial Area Functions
  4. Constructing Functions from Derivatives using Definite Integrals
  5. Fundamental Theorem of Calculus Part 2 (FTC 2): Evaluation
  6. FTC with Discontinuous Functions: Continuity vs. Differentiability

Study Notes

Introduction to Fundamental Theorem of Calculus Part 1 (FTC 1)

Let's break down what FTC 1 actually states.

If $f$ is a continuous function on an interval $[a, b]$, and we define a new function $F(x)$ as the definite integral of $f(t)$ from a constant $a$ to a variable $x$:

$F(x) = \int_a^x f(t) \, dt$

Then, FTC 1 states that the derivative of $F(x)$ with respect to $x$ is simply $f(x)$:

$F'(x) = \frac{d}{dx} \left[ \int_a^x f(t) \, dt \right] = f(x)$

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MATHS 105: common questions

What does MATHS 105 cover?

This MATHS 105 study guide covers 6 topics: Introduction to Fundamental Theorem of Calculus Part 1 (FTC 1), Continuity and Differentiability of Functions and Area Functions, Applications of FTC 1: Differentiating Partial Area Functions, Constructing Functions from Derivatives using Definite Integrals, Fundamental Theorem of Calculus Part 2 (FTC 2): Evaluation, FTC with Discontinuous Functions: Continuity vs. Differentiability.

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How do I revise for my MATHS 105 exam?

Read the MATHS 105 note for each topic, then take its practice quiz: the questions you get wrong come back as flashcards until you know them. Save the course to get a revision plan built around your exam date.