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#1 Amna Super Moderator Join Date: Aug 2005 Location: Desert of Dream Posts: 2,927 Thanks: 446 Thanked 1,975 Times in 1,040 Posts         Revised Syllabus and Recommended Books of Applied Mathematics

PAPER: APPLIED MATHEMATICS (100 MARKS)

I. Vector Calculus (10%)
:- Vector algebra; scalar and vector products of vectors; gradient divergence and curl of a vector; line, surface and volume integrals; Greens, Stokes and Gauss theorems.

II. Statics (10%) :-
Composition and resolution of forces; parallel forces and couples; equilibrium of a system of coplanar forces; centre of mass of a system of particles and rigid bodies; equilibrium of forces in three dimensions.

III. Dynamics (10%)

• Motion in a straight line with constant and variable acceleration; simple harmonic motion; conservative forces and principles of energy.
• Tangential, normal, radial and transverse components of velocity and acceleration; motion under central forces; planetary orbits; Kepler laws;
IV. Ordinary differential equations (20%)
• Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear
• equations, Bernoulli and Riccati equations.
• Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters.
• Ordinary and singular points of a differential equation; solution in series; Bessel and Legendre equations; properties of the Bessel functions and Legendre polynomials.
V. Fourier series and partial differential equations (20%)
• Trigonometric Fourier series; sine and cosine series; Bessel inequality; summation of infinite series; convergence of the Fourier series.
• Partial differential equations of first order; classification of partial differential equations of second order; boundary value problems; solution by the method of separation of variables; problems associated with Laplace equation, wave equation and the heat equation in Cartesian coordinates.
VI. Numerical Methods (30%)
• Solution of nonlinear equations by bisection, secant and Newton-Raphson methods; the fixed- point iterative method; order of convergence of a method.
• Solution of a system of linear equations; diagonally dominant systems; the Jacobi and Gauss-Seidel methods.
• Numerical differentiation and integration; trapezoidal rule, Simpsons rules, Gaussian integration formulas.
• Numerical solution of an ordinary differential equation; Euler and modified Euler methods; Runge- Kutta methods.

1. An Introduction to Vector Analysis------------------------------------- Khalid Latif,

2. Introduction to Mechanics------------------------------------- --------- Q.K. Ghori

3. An Intermediate Course in Theoretical Mechanics---------------------Khalid Latif,

4. Differential Equations with Boundary Value Problems----------------D. G. Zill and M. R. Cullen

5. Elementary Differential Equations--------------------------------------E.D. Rainville, P.E. Bedient and R.E. Bedient

6. Introduction to Ordinary Differential Equations---------------------- A.L.Rabenstein

8. An Introduction to Numerical Analysis-------------------------------- Mohammad Iqbal

9. Numerical Analysis------------------------------------- ----------------R.L Burden and J.D Faires

10. Elements of Numerical Analysis------------------------------------- -F. Ahmad and M.A Rana

11. Mathematical Methods------------------------------------- ----------S. M. Yousaf, Abdul Majeed and Muhammad Amin
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 The Following User Says Thank You to Amna For This Useful Post: hayya (Sunday, October 01, 2017)
#2
 Norymberskie Senior Member Join Date: May 2015 Posts: 277 Thanks: 14 Thanked 94 Times in 78 Posts  There are some good books in that list so I don't think we need to look anywhere else other than this list.

However, I would love to see someone post an analysis of a few books and tell us how much of the syllabus that book covers(with a list of chapters to do).

I have opted Pure and Applied Maths and will get started with QK Ghori book.
 The Following User Says Thank You to Norymberskie For This Useful Post: hayya (Sunday, October 01, 2017)

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