PHY 158 — MATHEMATICS FOR PHYSICS II
BSc BSc Physics · Kwame Nkrumah University of Science and Technology
Riemann integrability. Property of the Riemann integral. The fundamental theorem of integral calculus. Evaluation of integrals.. Connection of the trigonometric functions with the unit circle, the unit equilateral hyperbola and the hyperbolic functions. Properties of the hyperbola and the hyperbolic functions. Inverse hyperbolic functions. Differentiation and integration of the hyperbolic functions. The Riemann sum and the expression of the limit at infinity of certain series in integrals. Cauchy’s fundamental theorem of calculus. Classification and solution of differential equations (DE’s) of the first order. Linear differential equations (LDE’s) of first order. Equations reducible to first – order DE’s. LDE’s of arbitrary order; solution of second-order LDE’s with constant coefficients. Operational calculus and the solution of LDE’s with constant coefficients. Laplace transformations and their application to the solution of second-order LDE’s with constant coefficients. Solution of Euler – type DE’s. Applications to Mechanics. Vectors in Cartesian coordinate systems. Addition and multiplication of such matrix. Change of coordinate axes and the concept of matrices. Matrix algebra. Repeated rotations. Matrix multiplication. Types of matrices: orthogonal, hermitian and unitary matrices. Associated matrices: the transpose, adjoint and inverse of a matrix. The invariants of a matrix: the trace and determinant. Projectiles and evaluation of determinants. Application to the solution of simultaneous linear equations and linear systems of differential equations with constant coefficients
- Credits
- 2
- Level
- Level 100
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- ENGL 157 — Communication Skills I
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- FC 181 — FRENCH FOR COMMUNICATION
- FC 182 — FRENCH FOR COMMUNICATION II
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- PHY 152 — GEOMETRICAL OPTICS AND WAVES
- PHY 153 — ELECTRICITY AND MAGNETISM
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