Differentiation: The Derivative as a Function – Differentiation Rules – The Derivative as a Rate of Change – Derivatives of Trigonometric Functions – The ChainRule and Parametric Equations – Implicit Differentiation – Linearization and Differentials.

Chapter 2 – Sec: 2.1 to 2.7 and

Chapter 3 – Sec: 3.1 to 3.6, 3.7, SelfStudy – Sec: 3.7.

Application of Derivatives: Extreme values of Functions – The Mean Value Theorem – Monotonic Functions and the First Derivative Test – Concavity and Curve Sketching – Intermediate Forms and L’ Hospital’s Rule – Anti Derivatives.

Chapter 4 – Sec: 4.1 to 4.4, 4.6 to 4.8, SelfStudy – Sec: 4.5

The Definite Integral – The Fundamental Theorem of Calculus – Indefinite Integrals and the Substitution Rule – Substitution and Area between Curves.

Chapter 5 – Sec: 5.1 to 5.6

Techniques of Integration: Basic Integration Formulas – Integration by Parts – Integration of Rational Functions by Partial Fractions – Trigonometric Integrals – Trigonometric Substitutions – Numerical Integration – Improper Integrals.

Chapter 8: 8.1 to 8.5, 8.7,8.8, SelfStudy – Sec: 8.6

Application of Definite Integrals: Volumes by Slicing and Rotation about an Axis – Volumes by Cylindrical Shells – Lengths of Plane Curves – Moments and Centre of Mass – Areas of Surface of Revolution and the Theorems of Pappus – Work – Fluid Pressure and Forces.

Chapter 6 – Sec: 6.1 to 6.7

1. Finney and Thomas, “Calculus”, Pearson, Eleventh Edition, 2008.

References

1. Howard Anton, IRl Bivens, Stephens Davis, “Calculus” Wiley, 10th Edition, 2016 Reprint.
2. M. J. Strauss, G. L. Bradley and K. J. Smith, “Calculus”, 3rd Edition, Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), 2007.
3. James Stewart, “Calculus: Early Transcendentals”, Cengage (India), 8th Edition, 2016.