Course

Unit 1

LIMITS AND CONTINUITY

Shifting and Scaling of Graphs – Rates of Change and Limits –   Limits of Function Values – Calculating Limits Using the Limit Laws – Continuity – Tangents and Derivatives. (Chapter 1- Sec: 1.5, Chapter 2-Sec: 2.1, 2.2, 2.6 and 2.7)

Unit 2

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 – Linearization and Differentials. (Chapter 3- Sec: 3.1 to 3.6, 3.7, Self-Study – Sec: 3.7)

Unit 3

APPLICATION OF DERIVATIVES

Extreme values of Functions – The Mean Value Theorem – Monotonic Functions and the First Derivative Test – Concavity and Curve Sketching – Anti Derivatives. (Chapter 4- Sec: 4.1 to 4.4 and 4.8)

Unit 4

THE DEFINITE INTEGRAL

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. Basic Integration Formulas – Integration by Parts – Integration of Rational Functions by Partial Fractions – Trigonometric Integrals – Trigonometric Substitutions – Improper Integrals. (Chapter 5- Sec: 5.1 to 5.6, 8.1 to 8.5, 8.8)

Unit 5

APPLICATIONS OF DEFINITE INTEGRALS

Volumes by Slicing and Rotation About an Axis – Solids of Revolution: The Disk Method–Solids of Revolution: The Washer Method–Volumes by Cylindrical Shells–The Shell Method–Slope Fields and Separable Differential Equations –First-Order Linear Differential Equations. (Chapter 6- Sec: 6.1 to 6.2, Chapter 9- Sec: 9.1 to 9.2).

Text Books / References

Text Books:

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

References

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

This course introduces the fundamentals of calculus through hands-on learning using any mathematical software. Topics include various concepts from differential calculus and integral calculus. Lab exercises provide graphical understanding about the topics

Course Outcomes: After successful completion of the course, students will be able to

• CO1 : Improving the skills of visual understanding of the graph of the function and the concepts of limit, continuity and differentiability.
• CO2 : Understanding the basic concepts of Derivative of a function.
• CO3:  Applying the knowledge of derivative of a function to identify extreme values and concavity.
• CO4 : Understanding the concept of integration and apply the same to evaluate the area between curves.
• CO5 : Applying the concept of differentiation and integration in application related problems in science and engineering.

CO-PO Mapping: