i) Vector: scalars and vectors, component of a vector, rules of vector arithmetic, norm of a vector, normalizing of vectors, dot product, cross product, product of three or more vectors, equations of lines in space, planes in 3-space.

(ii) Vector-valued functions: limits and continuity, derivatives, forms of a curve equation in space, parametric representation, unit tangent and normal vectors, curvature, radius of curvature, motion  along a curve, velocity, acceleration and speed, normal and tangential components of acceleration.

(iii) Partial differentiation: Function of two or more variables, limits and continuity, partial derivatives, partial derivatives of functions of two variables, partial derivatives of functions with more than two variables, the chain rule, the chain rule for derivatives, the chain rule for partial derivatives, directional derivatives and gradients, directional derivatives, the gradient, tangent plans and normal vectors, maxima and minima of functions of two variables, Lagrange multipliers.

(iv) Multiple integrals: Double integral, areas and volumes, double integral in polar coordinates, parametric surfaces, surface area, surface integrals, evaluation of volume and triple integral.


1) James Steward, Calculus: Concepts and Contexts

2) James Steward, Multivariable Calculus

3) Helping Engineers Learn Mathematics (HELM)

4)  Kreysig, Advanced Engineering Mathematics, 9th edition, Wiley International