Higher Mathematics 3

Prof. Dr.-Ing. Dieter Kraus
   
9. Integration Calculus for Functions of several Variables (pdf)
   9.1 Integration over Intervalls
   9.2 Integration over Sets
   9.3 Applications
         9.3.1 Calculation of the Centroid
         9.3.2 Calculation of the Moment of Inertia

10. Ordinary Differential Equations (pdf)
   10.1 Introduction
   10.2 First-order Ordinary Differential Equations
         10.2.1 Geometric Interpretation
         10.2.2 Existence and Uniqueness of Solutions
         10.2.3 Separable Differential Equations
         10.2.4 Substitution Techniques
         10.2.5 First-order Linear Differential Equations
         10.2.6 Exact Differential Equations
         10.2.7 Integrating Factor Technique
         10.2.8 Bernoulli Differential Equation
         10.2.9 Riccati Differential Equation
   10.3 Higher-order Linear Differential Equations
         10.3.1 Basics
         10.3.2 Reduction of Order
         10.3.3 Linear Differential Equations with constant Coefficients
   10.4 Systems of First-order Linear Differential Equations
         10.4.1 Basics
         10.4.2 Systems of first-order lineare homogeneous Differential Equations with constant Coefficients

11. Laplace Transform (pdf)
   11.1 Basics
   11.2 Properties of the Laplace Transform
   11.3 Applications of the Laplace Transform
   11.4 Convolution Property

12. Difference Equations, z-Transform (pdf)
   12.1 Introduction to Difference Equations
   12.2 Linear Difference Equations
         12.2.1 Solution of  linear homogeneous Difference Equations
         12.2.2 Particular Solution of linearer homogeneous Difference Equations
   12.3 z-Transform
   12.4 Application of the z-Transform to linear inhomogeneous Difference Equations

13. Vector Analysis (pdf)
   13.1 Vector Fields
   13.2 Line Integrals
   13.3 Potentials
   13.4 Surface Area and Surface Integral
   13.5 Integral Theorems
         13.5.1 Green's Integral Theorem 
         13.5.2 Stokes' Integral Theorem
         13.5.3 Gauss' Integral Theorem
   13.6 Solinoidal Fields