What would you recommend as the best book for engineering in mathematics? Something with a great insight and depth, and very well explained. With good exercises too. Here's the chapter it's required to have: Partial Differentiation: Introduction to Partial differentiation, Total derivative, Differentiation of implicit functions, Geometrical interpretation, Tangent plane and normal to a surface, Change of variables, Jacobians, Taylor’s theorem for functions of two variables. Applications Of Partial Differentiation : Total differential, Maxima and minima of functions of two variables, Lagrange’s method of undetermined multipliers, Differentiation under the integral sign, Leibnitz’s Rule. Partial Differential Equations : Introduction, Formation of partial differential equations, Solutions of a partial differential equation, Equations solvable by direct integration, Linear equations of the first order, Nonlinear equations of the first order, Homogeneous linear equations with constant coefficients, Rules for finding the complementary function, Rules for finding the particular integral. Linear Algebra-1: Rank of Matrix, Elementary transformations, Elementary matrices, Inverse, Normal form, Consistency of linear system of equations, Linear transformations. Linear Algebra – 2: Eigen value and eigen vectors of a matrix, Cayley-Hamilton theorem, Reduction to diagonal form, Quadratic forms and canonical forms, Hermitian and Skew Hermitian matrix, Unitary matrix.