COURSE SUMMARY
Course Title:
Calculus
Course Code:
18MAT101
Year Taught:
2019
Semester:
1
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'Calculus' is a course offered in First Semester of B. Sc. - B. Ed. in Physics, Mathematics, Computer Science program at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

#### Scope and Objectives

On completion of the course, the student teacher will;

To enable students to understand the meaning of differentiation and integration and apply the techniques of indefinite and definite integration.

#### Syllabus

Unit I:

• Limits and continuity: Rates of Change and Limits – Calculating Limits using Limiting Laws – The Precise definition of Limit – One-Sided Limits and Limits at Infinity – Continuity – Tangents and Derivatives.
• Chapter-2 (Sections 2.3-2.7).

Unit II:

• Differentiation: The Derivative as a Function – Differentiation Rules – The Derivative as a Rate of Change – Derivatives of Trigonometric Functions – The Chain Rule and Parametric Equations – Implicit Differentiation -nth derivatives of the functions: eax , (ax + b)n , log(ax + b), sin(ax + b) , cos(ax + b), eaxsin(bx+ c), eaxcos(bx + c) – Problems.
• Chapter-3 (Sections 3.1-3.6).

Unit III:

• Application of Derivatives: Extreme values of Functions – The Mean Value Theorem – Monotonic Functions and the First Derivative Test – Concavity and Curve Sketching.
• Chapter-4 (Sections 4.1-4.4).

Unit IV:

• Integration: Estimating with Finite Sums – Sigma Notation and Limits of Finite Sums – The Definite Integral – The Fundamental Theorem of Calculus – Indefinite Integrals and the Substitution Rule – Substitution and Area between Curves.
• Chapter-5 (Sections 5.1-5.6).

Unit V:

• Techniques of Integration: Basic Integration Formulas – Integration by Parts – Integration of Rational Functions by Partial Fractions – Trigonometric Integrals – Trigonometric Substitutions– Improper Integrals.
• Chapter-8 (Sections 8.1-8.4, 8.8).

#### Textbook

1. Calculus by Finney and Thomas, Pearson, Eleventh Edition, 11th Edition, Pearson, 2009.

#### References

1. M. J. Strauss, G. L. Bradley and K. J. Smith, Calculus, 3rd Edition, Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), 2007.
2. S Balachandra Rao, Differential Calculus, New Age Publications, 2005.