# Engineering Mathematics III KNEC Notes and Syllabus 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 