Calculus

Open course material *Calculus* offered by the Teaching and Learning Centre of FNWI.

Auteurs: André Heck, Marthe Schut

Available languages:

Course content

Functions and graphs

Relations and functions

Function machines and composition of functions

Data and graphs

Properties of functions

Transformations of graphs and functions

Basic functions

Power functions

Linear functions

Polynomial functions

Rational functions

Exponential functions and logarithms

Exponential functions

PRACTICE

P

9.

Equations and inequalities with exponential functions that have the same base

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Logarithms

PRACTICE

P

11.

Solving equations and inequalities with logarithms that have the same base

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PRACTICE

P

13.

Solving equations and inequalities that contain logarithms with different bases

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Trigonometry

Trigonometric functions

Inverse trigonometric functions

Parametric curves

Plane curves

Polar coordinates and polar curves

Space curves

Differentiation, derivatives and Taylor approximations

Tangent line

Differentiating power functions

Rules for differentiating functions

Differentiating implicit functions

Differentiating exponential and logarithmic functions

Differentiating trigonometric functions and their inverse functions

Higher-Order derivatives

Applications of derivatives

Taylor approximations

Numerical differentiation

Time series

Difference formulas for the first derivative

Difference formulas for the second derivative

Iteration of functions

Iteration of functions and fixed points

Finding zeros via iterations

Finding zeros via the Newton-Raphson method

Limits part 1: Infinite sequences

Introduction

Basic calculation rules for limits

Techniques

Standard limits

Final paragraph

Limits part 2: Functions

All kinds of limits

Techniques

Final paragraph

Infinite series

Introduction

Common series

Convergence tests

Final chapter

Differentials and integrals

Differentials

Area and primitive function

Indefinite integrals

Integration techniques

Applications of integration

Improper integrals

Numerical Integration

Some Riemann sums

The trapezoidal rule

Computer inquiry into efficiency of numerical integration methods

Unlimited growth

Linear and quadratic growth

Exponential growth

Applications of exponential growth models

Limited exponential growth

Introduction

Limited exponential growth functions

Applications of limited exponential growth models

Logistic growth

Introduction

The logistic function

More examples of logistic growth