Revised Syllabus and Recommended Books of Applied Mathematics
 

[CENTER][FONT=Verdana][SIZE=3][COLOR=Green][B]PAPER: APPLIED MATHEMATICS (100 MARKS) [/B]
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[B]I. Vector Calculus (10%)[/B][/SIZE][/FONT][SIZE=3] [FONT=Verdana] :- 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.

[B] II. Statics (10%) :-[/B][/FONT] [FONT=Verdana] 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.

[B] III. Dynamics (10%) [/B][/FONT] [FONT=Verdana]
[/FONT][/SIZE][LIST][*][SIZE=3][FONT=Verdana]Motion in a straight line with constant and variable acceleration; simple harmonic motion; conservative forces and principles of energy. [/FONT][/SIZE][/LIST][LIST][*][SIZE=3][FONT=Verdana]Tangential, normal, radial and transverse components of velocity and acceleration; motion under central forces; planetary orbits; Kepler laws; [/FONT][/SIZE][/LIST][SIZE=3][FONT=Verdana][B] IV. Ordinary differential equations (20%) [/B][/FONT] [FONT=Verdana]
[/FONT][/SIZE][LIST][*][SIZE=3][FONT=Verdana]Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear [/FONT][/SIZE][/LIST][LIST][*][SIZE=3] [FONT=Verdana]equations, Bernoulli and Riccati equations. [/FONT][/SIZE][/LIST][LIST][*][SIZE=3][FONT=Verdana]Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters. [/FONT][/SIZE][/LIST][LIST][*][SIZE=3][FONT=Verdana]Ordinary and singular points of a differential equation; solution in series; Bessel and Legendre equations; properties of the Bessel functions and Legendre polynomials. [/FONT][/SIZE][/LIST][SIZE=3][FONT=Verdana][B] V. Fourier series and partial differential equations (20%) [/B][/FONT] [FONT=Verdana]
[/FONT][/SIZE][LIST][*][SIZE=3][FONT=Verdana]Trigonometric Fourier series; sine and cosine series; Bessel inequality; summation of infinite series; convergence of the Fourier series. [/FONT][/SIZE][/LIST][LIST][*][SIZE=3][FONT=Verdana]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. [/FONT][/SIZE][/LIST][SIZE=3][FONT=Verdana][B] VI. Numerical Methods (30%) [/B][/FONT] [FONT=Verdana]
[/FONT][/SIZE][LIST][*][SIZE=3][FONT=Verdana]Solution of nonlinear equations by bisection, secant and Newton-Raphson methods; the fixed- point iterative method; order of convergence of a method. [/FONT][/SIZE][/LIST][LIST][*][SIZE=3][FONT=Verdana]Solution of a system of linear equations; diagonally dominant systems; the Jacobi and Gauss-Seidel methods. [/FONT][/SIZE][/LIST][LIST][*][SIZE=3][FONT=Verdana]Numerical differentiation and integration; trapezoidal rule, Simpson’s rules, Gaussian integration formulas. [/FONT][/SIZE][/LIST][LIST][*][SIZE=3][FONT=Verdana]Numerical solution of an ordinary differential equation; Euler and modified Euler methods; Runge- Kutta methods. [/FONT][/SIZE][/LIST][SIZE=3] [FONT=Verdana]
[/FONT][/SIZE] [CENTER][CENTER][FONT=Verdana][SIZE=5][COLOR=Green][B]SUGGESTED READINGS[/B][/COLOR][/SIZE][/FONT][/CENTER]
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[FONT=Verdana][SIZE=3] 1. An Introduction to Vector Analysis[COLOR=white]------------------------------------- [/COLOR] Khalid Latif,

2. Introduction to Mechanics[COLOR=white]------------------------------------- ---------[/COLOR] Q.K. Ghori

3. An Intermediate Course in Theoretical Mechanics[COLOR=white]---------------------[/COLOR]Khalid Latif,

4. Differential Equations with Boundary Value Problems[COLOR=white]----------------[/COLOR]D. G. Zill and M. R. Cullen

5. Elementary Differential Equations[COLOR=white]--------------------------------------[/COLOR]E.D. Rainville, P.E. Bedient and R.E. Bedient

6. Introduction to Ordinary Differential Equations[COLOR=white]----------------------[/COLOR] A.L.Rabenstein

7. Advanced Engineering Mathematics[COLOR=white]-----------------------------------[/COLOR]E. Kreyszig

8. An Introduction to Numerical Analysis[COLOR=white]--------------------------------[/COLOR] Mohammad Iqbal

9. Numerical Analysis[COLOR=white]------------------------------------- ----------------[/COLOR]R.L Burden and J.D Faires

10. Elements of Numerical Analysis[COLOR=white]------------------------------------- -[/COLOR]F. Ahmad and M.A Rana

11. Mathematical Methods[COLOR=white]------------------------------------- ----------[/COLOR]S. M. Yousaf, Abdul Majeed and Muhammad Amin[/SIZE][/FONT]

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.