Unit I
The Precise definition of a Limit – One-Sided Limits and Limits at Infinity – Infinite Limits and Vertical Asymptotes – Continuity – Tangents and Derivatives.
(Sections 2.1, 2.3-2.7)
| Course Name | Calculus |
| Course Code | 25MAT101 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | 1 |
| Credits | 4 |
| Campus | Mysuru |
The Precise definition of a Limit – One-Sided Limits and Limits at Infinity – Infinite Limits and Vertical Asymptotes – Continuity – Tangents and Derivatives.
(Sections 2.1, 2.3-2.7)
Extreme values of Functions – The Mean Value Theorem – Monotonic Functions and the First Derivative Test – Concavity and Curve Sketching – Integration-Riemann Sum – Definite integrals – The Fundamental Theorem of Calculus.(Sections 4.1-4.4, 5.2-5.4)
Functions in Several Variables – Limits and Continuity in Higher Dimensions – Partial Derivatives – Chain Rule – Directional Derivatives and Gradients – Tangent Planes and Differentials – Extreme Values and Saddle Points – Lagrange Multipliers. (Sections 14.1-14.8)
Line integrals – Vector fields, Work, Circulation and Flux – Path Independence, Potential Functions and Conservative Fields – Green’s Theorem in the Plane.
(Sections 16.1-16.4)
Surface Areas and Surface Integrals – Parameterized Surfaces – Orientation of Surfaces – Stoke’s Theorem and Divergence Theorem.
(Sections 16.5-16.8)
Course Objectives:
Course Outcomes
| COs | Description |
| CO1 | Recognize and determine infinite limits and limits at infinity and interpret with respect to asymptotic behavior. |
| CO2 | Determine the derivative and higher derivatives of a function explicitly using differentiation formulas. |
| CO3 | Explain and apply the concepts extreme values and Lagrange multipliers for simple optimization problems. |
| CO4 | Explain and apply the concepts line and double integrals to various problems including Green’s theorem for plane |
| CO5 | Explain the concepts of surface integrals, divergence theorem and Stokes theorem. |
CO-PO Mapping
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PSO1 |
PSO2 |
PSO3 |
PSO4 |
| CO | ||||||||||||||
| CO1 | 2 | – | 2 | 3 | 3 | – | 1 | – | – | – | – | 1 | 2 | – |
| CO2 | 3 | – | 1 | 3 | 2 | – | 1 | – | – | – | – | 1 | 3 | – |
| CO3 | 2 | – | 2 | 3 | 2 | – | 1 | – | – | – | – | 1 | 2 | – |
| CO4 | 2 | – | 2 | 3 | 3 | – | 1 | – | – | – | – | 1 | 3 | – |
| CO5 | 2 | – | 3 | 3 | 2 | – | 1 | – | – | – | – | 1 | 2 | – |
TextBooks:
1) G.B. Thomas and R.S. Finney, Calculus, 11th Edition, Pearson, 2009.
REFERENCES:
1) Monty J. Strauss, Gerald J. Bradley and Karl J. Smith, Calculus, 3rd Edition, 2002.
2) Dennis G. Zill and Michael R.Cullen, Advanced Engineering Mathematics, 2nd edition, CBS Publishers, 2012.
3) Srimanta Pal and Subhodh C Bhunia, Engineering Mathematics, 9th edition, John Wiley and Sons, 2012.
4) James Stewart, Calculus: Early Transcendentals, 8th Edition, Cengage (India), 2016.
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