Higher Mathematics 2

Prof. Dr.-Ing. Dieter Kraus
   
5. Integral Calculus (pdf)
   5.1 Basics
         5.1.1 Upper Sum / Lower Sum
         5.1.2 Riemann Sum
         5.1.3 Properties of the Integral
         5.1.4 Integration on Subintervals
   5.2 Fundamental Theorem of Calculus
   5.3 Special Methods of Integration
         5.3.1 Integration by Parts
         5.3.2 Change of Variable
   5.4 Integration of special Functions
         5.4.1 Integration of rational Functions
         5.4.2 Integrals of the Form R(sinx,cosx) dt
   5.5 Supplementary Considerations
         5.5.1 Integration of even and odd Functions
         5.5.2 Calculation of Areas
         5.5.3 Mean Value Theorem
   5.6 Improper Integrals
   5.7 Some Applications
         5.7.1 Arc length of a plane Curve
         5.7.2 Volumen of Revolution
         5.7.3 Surface of Revolution
   5.8 Numerical Integration
         5.8.1 Rectangular Rule
         5.8.2 Trapezoidal Rule
         5.8.3 Simpson's Rule

6. Series (pdf)
   6.1 Infinite Series
         6.1.1 Introduction
         6.1.2 Properties of infinite Series
         6.1.3 Convergence Test
         6.1.4 Properties of absolutely convergent Series
   6.2 Power Series
         6.2.1 Introduction
         6.2.2 Properties of Power Series
         6.2.3 Operations with Power Series
   6.3 Uniform Convergence
         6.3.1 Sequences of Functions
         6.3.2 Series of Functions
   6.4 Taylor Expansion
         6.4.1 Taylor Formula
         6.4.2 Taylor Series
      
7. Differential Calculus for Functions of several Variables (pdf )
   7.1 Introduction
   7.2 Properties of the Rn
   7.3 Sequences in the Rn
   7.4 Continuity of Functions of several Variables
   7.5 Directional Derivative, Partial Derivative
   7.6 Differentiation under the Intergral Sign
   7.7 High Order Partial Derivation
   7.8 Vector valued Functions
   7.9 Chain Rule
   7.10 Taylor Series in several Variables
   7.11 Implicit Functions
   7.12 Extrema for Functions of several Variables

8. Fourier Analysis (pdf)
   8.1 Basics
   8.2 Fourier Series
         8.2.1 Real Representation of the Fourier Series
         8.2.2 Complex Representation of the Fourier Series
   8.3 Fourier Integral