Course Title: MATH 157
Type of Course: Compulsory, Theory, Non-departmental
Offered to: EEE
Pre-requisite Course(s): None
Differential Calculus: Limits, continuity and differentiability. Successive differentiation of various types of functions. Leibnitz's theorem. Rolle's theorem, Meanvalue theorem, Taylor's and Maclaurin’s theorems in finite and infinite forms. Lagrange's form of remainder. Cauchy's form of remainder. Expansion of functions. Evaluation of indeterminate forms by L'Hospital's rule. Partial differentiation, Euler's theorem. Tangent and Normal. Sub tangent and subnormal in Cartesian and polar coordinates. Determination of maximum and minimum values of functions. Curvature. Asymptotes and curve tracing.
Integral Calculus: Integration by the method of substitution. Standard integrals. Integration by successive reduction. Definite integrals, its properties and use in summing series. Walli's formulae. Improper integrals. Beta function and Gamma function. Area under plane curves and area of a region enclosed by two curves in Cartesian and polar coordinates. Volume and surface area of solids of revolution.
To provide the appropriate tools of calculus to solve applied problems.
To provide the standard methods of indefinite and definite integrals with their applications.
Familiarity with basic properties of set theory and function; fundamental concepts of pre-calculus and preliminary knowledge to solve algebraic and transcendental equations.
| CO No. | CO Statement | Corresponding PO(s)* | Domains and Taxonomy level(s) | Delivery Method(s) and Activity(-ies) | Assessment Tool(s) | |
|---|---|---|---|---|---|---|
| 1 | Explain the fundamental concepts of limits, derivatives, and expansion of functions. | PO(b) | C2 | Lectures, Homework | Written exams, Assignment |
|
| 2 | Demonstrate the idea of indefinite and definite integrals to evaluate integrals | PO(a) | C3 | Lectures, Homework | Written exams, Assignment |
|
| 3 | Apply the idea of accumulation to calculate area, volume and surface area. | PO(b) | C3 | Lectures, Homework | Written exams, Assignment |
|
Cognitive Domain Taxonomy Levels: C1 – Knowledge, C2 – Comprehension, C3 – Application, C4 – Analysis, C5 – Synthesis, C6 – Evaluation, Affective Domain Taxonomy Levels: A1: Receive; A2: Respond; A3: Value (demonstrate); A4: Organize; A5: Characterize; Psychomotor Domain Taxonomy Levels: P1: Perception; P2: Set; P3: Guided Response; P4: Mechanism; P5: Complex Overt Response; P6: Adaptation; P7: Organization
Program Outcomes (PO): PO(a) Engineering Knowledge, PO(b) Problem Analysis, PO(c) Design/development Solution, PO(d) Investigation,
PO(e) Modern tool usage, PO(f) The Engineer and Society, PO(g) Environment and sustainability, PO(h) Ethics, PO(i) Individual work and team work,
PO(j). Communication, PO(k) Project management and finance, PO(l) Life-long Learning
* For details of program outcome (PO) statements, please see the departmental website or course curriculum
| K1 | K2 | K3 | K4 | K5 | K6 | K7 | K8 | P1 | P2 | P3 | P4 | P5 | P6 | P7 | A1 | A2 | A3 | A4 | A5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Weekly schedule: For Differential Calculus
| Weekly plan for course content and mapping with Cos | |
|---|---|
| Weeks | Topics |
| Week-1 to 2 | Limits, Continuity, and differentiability. |
| Week-3 to 4 | Successive differentiation of various types of functions. |
| Week-5 to 8 | Leibnitz's theorem. Rolle's theorem. Mean value theorem. Taylor's and Maclaurin’s theorems in finite and infinite forms. Lagrange's form of remainders. Cauchy's form of remainders. |
| Week -9 to 10 | Expansion of functions. Evaluation of indeterminate forms by L'Hospitals rule. Partial differentiation. Euler's theorem. |
| Week-11 to 12 | Tangent and Normal. Subtangent and subnormal in Cartesian and polar co-ordinates. curvature, Asymptotes. |
| Week-13 to 14 | Determination of Maximum and minimum values of functions with applications. |
Weekly schedule: For Integral Calculus
| Week | Topics |
|---|---|
| Week-1 | Integration by the method of substitution, |
| Week-2 | Standard integrals. |
| Week-3 | Integration by successive reduction. |
| Week-4 | Definite integrals, its properties |
| Week-5 | Use of definite integral in summing series. Walli's formulae. |
| Week-6 | Class test |
| Week-7 | Improper integrals. |
| Week-8 | Beta function and Gamma function. |
| Week-9 | Area under plane curves in Cartesian and polar coordinates |
| Week-10 | Area of a region enclosed by two curves in Cartesian and polar coordinates |
| Week-11 | Volume of solids of revolution. |
| Week-12 | Area of surface of revolution |
| Week-13 | Class Text |
| Week-14 | Review class |
Class Participation: Class participation and attendance will be recorded in every class.
Continuous Assessment: Continuous assessment for any of the activities such as quizzes, assignment, presentation etc. The scheme of the continuous assessment for the course will be declared on the first day of classes.
Final Examination: A comprehensive term final examination will be held at the end of the term following the guideline of academic council.
Class Participation 10%
Continuous Assessment 20%
Final Examination 70%
Total 100%
Calculus by Howard Anton, Irl Bivens and Stephen Davis.
Differential and Integral Calculus by B. C. Das and B. N. Mukherjee.
Integral Calculus with applications by A. K. Hazra
.