Engineering Mathematics III is a module III unit in electrical and electronic engineering. It is intended to increase knowledge, skills, and attitudes to enable learners to understand analytical areas.

Its prerequisites include Engineering Mathematics I and II.

**Topics to be Covered:**

**Topic 1: Vector Field Theory**

- Definition of dot and cross products of vectors
- Solution of problems involving dot and cross products vectors
- Definition of operators
- Definition of vector field
- Definition of curl F
- Solutions of problems involving curl F
- Solutions of problems involving F

**Topic 2: Matrices**

- Matrix operation
- Determinant of 3*3 Matrix
- Inverse of 3*3 Matrix
- Solution of linear simultaneous equations in 3 unknowns
- Application of matrices

**Topic 3: Numerical Methods**

- Definition of interpolation and extrapolation
- Application of interpolation and
- Application of interactive methods to solve equations
- Application of interactive methods to areas and volumes

**Topic 4: Double and Triple Integrals**

- Definition of double and triple integrals
- Use of multiple integrals to find areas and volume
- Consideration of double integrals in polar and cylindrical coordinates
- Use of triple integrals in solving problems

**Topic 5: Differential Equals**

- Types of first order differential equations
- Formation of first order differential equations
- Solutions of first order differential equations
- Application of first order differential equations
- Formation of the second order differential equations for various systems
- Solution of second order differential equations
- Application of second order differential equations

**Topic 6: Laplace Transforms**

- Definition of Laplace transforms
- Deriving Laplace transforms from first principles
- State properties of Laplace transform
- Determination of inverse LT of simple transforms and partial fractions
- Solution of differentiation equations by LT
- Solution of simultaneous differential equations by given initial conditions

**Topic 7: Fourier series**

- Determination of the fourier series as a periodic function of period 2 and extended to
- Determination of fourier series of non-periodic functions over a given range
- Determination of fourier for even and odd functions and the half-range series for given function

**Topic 8: Loci**

- Definition of a point
- Locus of a point in relation to a circle
- Loci of points for given mechanism