Calculus and linear algebra in recipes : terms, theorems and numerous examples in short learning units / Christian Karpfinger

Format:

Book

Author/Creator:

Karpfinger, Christian, 1968- author.

Language:

English

Subjects (All):

Calculus.

Algebras, Linear.

calculus.

Physical Description:

1 online resource (xx, 1049 pages) : illustrations

Edition:

Second edition

Place of Publication:

Berlin, Germany : Springer, [2026]

Summary:

"This book provides a clear and easy-to-understand introduction to higher mathematics with numerous examples. The author shows how to solve typical problems in a recipe-like manner and divides the material into short, easily digestible learning units. Have you ever cooked a 3-course meal based on a recipe? That generally works quite well, even if you are not a great cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise: Need to solve a Riccati's differential equation or the singular value decomposition of a matrix? Look it up in this book, you'll find a recipe for it here. Recipes are available for problems from the field of: · Calculus in one and more variables, · Linear algebra, · Vector analysis, · Theory on differential equations, ordinary and partial, · Theory of integral transformations, · Function theory. Other features of this book include: · The division of Higher Mathematics into approximately 100 chapters of roughly equal length. Each chapter covers approximately the material of a 90-minute lecture. · Numerous exercises and solutions · Many problems in higher mathematics can be solved with computers. We always indicate how it works with MATLAB®. This 2nd English edition has been completely revised and numerous examples, illustrations, explanations and further exercises have been added. Prof. Dr. Christian Karpfinger teaches at the Technical University of Munich; in 2004 he was awarded the State Teaching Award of the Free State of Bavaria"-- Springer Nature Link

Contents:

Terminology, symbols and sets

The natural numbers, integers and rational numbers

The real numbers

Machine numbers

Polynomials

Trigonometric functions

Complex numbers – Cartesian coordinates

Complex numbers – polar coordinates

Linear equation systems

Calculating with matrices

LR-decomposition of a matrix

The determinant

Vector spaces

Generating systems and linear (in-)dependence

Bases of vector spaces

Orthogonality I

Orthogonality II

The linear least squares problem

The QR-decomposition of a matrix

Sequences

Calculation of limits of sequences

Series

Mappings

Power series

Limits and continuity

Differentiation

Applications of differential calculus I

Applications of differential calculus II

Polynomial and spline interpolation

Integration I

Integration II

Improper integrals

Separable and linear first-order differential equations

Linear differential equations with constant coefficients

Some special types of differential equations

Numerics of ordinary differential equations I

Linear mappings and representation matrices

Basic transformation

Diagonalization – eigenvalues and eigenvectors

Numerical calculation of eigenvalues and eigenvectors

Quadrics

Schur decomposition and singular value decomposition

The Jordan normal form I

The Jordan normal form II

Definiteness and matrix norms

Functions of several variables

Partial differentiation – gradient, Hessian matrix, Jacobian matrix

Applications of partial derivatives

Determination of extreme values

Determination of extreme values under constraints

Total differentiation, differential operators

Implicit functions

Coordinate transformations

Curves I

Curves II

Curve integrals

Gradient fields

Area integrals

The transformation formula

Surfaces and surface integrals

Integral theorems I

Integral theorems II

Generalities on differential equations

The exact differential equation

Linear differential equation systems I

Linear differential equation systems II

Linear differential equation systems III

Boundary value problems

Basic concepts of numerics

Fixed point iteration

Iterative methods for linear equation systems

Optimization

Numerics of ordinary differential equations II

Fourier series – calculation of Fourier coefficients

Fourier series – background, theorems and application

Fourier transformation I

Fourier transformation II

Discrete Fourier transformation

The Laplace transformation

Holomorphic functions

Complex integration

Laurent series

The residue calculus

Conformal mappings

Harmonic functions and the Dirichlet boundary value problem

First-order partial differential equations

Second-order partial differential equations – general

The Laplace or Poisson equation

The heat conduction equation

The wave equation

Solving PDEs with Fourier- and Laplace transformations

Notes:

Includes index

Online resource; title from PDF title page (Springer Nature Link, viewed April 16, 2026)

Other Format:

Print version: Karpfinger, Christian, 1968- Calculus and linear algebra in recipes

ISBN:

9783662726235

3662726238

OCLC:

1586323126

Access Restriction:

Restricted for use by site license