I'm a first year maths student and need some help in finding the right textbook. This is the course synopsis:
General linear homogeneous ODEs: integrating factor for first order linear ODEs, second solution when one solution is known for second order linear ODEs. First and second order linear ODEs with constant coefficients. General solution of linear inhomogeneous ODE as particular solution plus solution of homogeneous equation. Simple examples of finding particular integrals by guesswork. Systems of linear coupled first order ODEs. Calculation of determinants, eigenvalues and eigenvectors and their use in the solution of linear coupled first order ODEs.
Parabolic, Spherical and Cylindrical polar coordinate systems. Introduction to partial derivatives. Chain rule, change of variable, Jacobians with examples including polar coordinate systems. Solving some simple partial differential equations.
Surfaces. Sketching simple quadrics. Gradient vector; normal to surface, directional derivative. Taylor's Theorem for a function of two variables (statement only). Critical points and classification using directional derivatives and Taylor's theorem. Informal (geometrical) treatment of Lagrange multipliers.
I'm not looking for an advanced book, but book for a beginner (which includes all those topics).