Robert Mařík's eReadings on Mathematics

course materials for Mathematics I and Mathematics II
for students of Faculty of Bussines and Economics
at Mendel University of Agriculture and Forestry Brno
Supported by the Grant No 18/2006 of Developement of Czech Universities

Sorted by topic
Sorted by form

By topic

Mathematics I
(differenatial calculus, linear algebra)

Mathematics II
(integral calculus, differential and difference equations,
numerical mathematics)

Differential calculus in one variable

Theory (precalculus, limits, derivatives)
Basic elementary functions - short overview
Calculator - function tables
Animations on slopes, limits and tangent, definition of limit and derivative.
Pictures

x and y intercepts
graph1 (finding value)
graph2 (solving equation)
graph3 (solving inequality)
Monotonicity
One-to-one function
Jump, removable and essential discontinuities
Asymptotes
Theorem of Bolzano
Continuous function

Solved problems

Quizzes

Functions - basic properties

Inverse functions

Real world applications

Optimal values of a function

Related rates

Man walking below a lamp

Shadow of a falling ball

Linear approximation

Refference cards

eCards

Jeopardy game

Differential calculus in two varaibles

Theory on multivariable calculus
Solved problems

Pictures

Quizzes

eCards

Partial derivatives

Linear algebra

Theory and Solved problem from linear algebra
Calculator for matrix row operations
Real world application: heat conduction

Integral calculus

Theory and Solved problems

Indefinite integral

Riemann integral

Improper integral

Refference cards

Real world applications

Quizzes

Mathematical games

First ordinary differential equations (ODE)

Theory and Solved problem on first order differential equations
Pictures

Real world applications

Suspension bridge and hanging chains

Social diffusion

Quizzes - First order differential equations

ODE with separated variables

Linear ODE - formula

Linear ODE - variation of constants

Matching game - separated ODE's

Second order ODE

Theory and Solved problems on second order differential equations
Quizzes - Second order differential equations

Homogeneous equations

Guessing particular solution

Particular solution by variation of constants

Particular solution by variation of constants and Wronskian

Refference card
Math game - linear, second order equations

Difference equations

Theory and Solved problems on difference equations
Real world applications

Cobweb cycles in economics

Numerical mathematics

Algebraic equations and Lagrange polynomial

Introduction - Jeopardy game

Theory and Solved problems on algebraic equations and Lagrange polynomial
Pictures

Calculators for Horner's scheme and bisection of interval

Taylor polynomial

Theory and Solved problems on Taylor polynomial
Real world applications and math. applications

Least squares

Theory and Solved problems on least squares method
Picture - least squres and cost function
Calculator for the best linear fit

By form

Noninteractive documents

Interactive documents

Theory and Solved problems

Calculus

Theory for precalculus, limits, derivatives

Limits

Derivatives

Limits and l'Hospital rule

Local extrema in one varaible

Graphing functions

Multivariable calculus

Integral calculus

Indefinite integral

Riemann integral

Improper integral

Linear algebra

Linear algebra

Differential equations

First order differential equations

Second order differential equations

Numerical mathematics

Algebraic equatinos and Lagrange polynomial

Taylor polynomial

Least squares

Refference cards
Real world applications

Pictures

Calculus

x and y intercepts

graph1 (finding value)

graph2 (solving equation)

graph3 (solving inequality)

Monotonicity
One-to-one function
Jump, removable and essential discontinuities
Asymptotes
Theorem of Bolzano

Numerical mathematics

Differential equations

Pictures for multivariable calculus

Calculators

Quizzes

Differential calculus in one and two variables

Limits from graphs

Derivatives

Local extrema in one variable

Partial derivatives

Local extrema in two variables

Integral calculus

Formulas

Integrals of partial fractions

Decomposition into partial fractions

Rational functions

Integration by parts

Integration by substitution

Riemann integral

Summary - methods of integral calculus

First order ODE

ODE with separated variables

Linear ODE - formula

Linear ODE - variation of constants

Second order linear ODE with constant coefficients

Homogeneous equations

Guessing particular solution

Particular solution by variation of constants

Particular solution by variation of constants and Wronskian

eCards

Mathematical games

Derivative - product rule
Integrals

Differential equations

Jeopardy games