Limits and Continuity

Introduction to Limits

Rates of Change and Limits

One-Sided Limits, Infinite Limits

Continuity, Continuity at a Point, Continuity on an interval

Differentiation

Definition and Examples

                   Relation Between Differentiability and Continuity

                  Derivative as slope, as rate of change (graphical representation).

                 The Chain Rule

                Applications of Ordinary Derivatives

               Integration

               Indefinite Integrals

              Different Techniques for Integration

              Definite Integrals

              Riemann Sum, Fundamental Theorem of Calculus

              Area Under the Graph of a Nonnegative Function

              Improper Integrals

           Transcendental Functions

            Inverse functions

            Logarithmic and Exponential Functions

            Inverse Trigonometric Functions

           Hyperbolic Functions and Inverse Hyperbolic Functions

            More Techniques of Integration

            Analytical Geometry

        Three Dimensional Geometry

         Vectors in Spaces

        Vector Calculus

        Directional Derivatives

       Divergence, Curl of a Vector Field

        Multivariable Functions

        Partial Derivatives

        Conic Sections

       Parameterizations of Plane Curves

        Vectors in Plane, Vectors in space

        Dot Products, Cross Products

        Lines and Planes in Space

       Spherical, Polar and Cylindrical Coordinates.

       Vector-Valued Functions and Space Curves

      Arc-Length and Tangent Vector

     Curvature, Torsion and TNB Frame

    Fubini’s Theorem for Calculating Double Integrals

   Areas Moments and Centers of Mass

   Triple Integrals and volume of a region in space

   Recommended Books

1.   Thomas’ Calculus by J. R. Hass, C. D. Heil and M. D. Wier, 14th edition, Pearson, ISBN 978 0134438986

2.   Essential Calculus by James Stewart, 2nd Edition, ISBN 978-1133112297

3.   Advanced Engineering Mathematics by Erwin Kreyszig, 10th Ed. Willey 2014. ISBN 978-0-470-91361-1