APPLIED MATHEMATICS - I
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| UP Polytechnic/Diploma In Computer Science And Engineering Applied Mathematics - I Syllabus 2023 - 24 - EdufyHUB 4U |
RATIONALE
Contents of this course provide fundamental base for understanding elementary mathematics and their uses in solving engineering problems. Contents of this course will enable students to use basic mathematical function like logarithms, partial fractions, matrices and basic 2D, curves in solving various engineering problems of all fields.
LEARNING OUTCOMES
After undergoing the subject, the students will be able to:
- Apply binomial theorem to solve engineering problems
- Apply determinants properties and crammer’s rule to solve engineering problems
- Apply dot & cross product of vectors to find the solution of engineering problems
- Use complex numbers in various engineering problems
- Apply differential calculus and higher order to solve engineering problems
- Find velocity, acceleration, errors and approximation in engineering problems with Application of derivatives.
DETAILED CONTENTS
1. Algebra -I
(12 Periods)
- 1.1 Series:
- AP And GP
- Sum
- nth term
- Mean
- 1.2
- Binomial Theorem For Positive
- Negative And Fractional Index (Without Proof)
- Application Of Binomial Theorem
- 1.3 Determinants:
- Elementary Properties Of Determinant Of Order 2 And 3
- Multiplication System Of Algebraic Equation
- Consistency Of Equation
- Crammer's Rule
2. Algebra -II
(12 Periods)
- 2.1 Vector Algebra:
- Dot And Cross Product
- Scaler And Vector Triple Product
- 1.3 Complex Number:
- Complex Number
- Representation
- Modulus And Amplitude Demoivre Theorem
- Its Application In Solving Algebraic Equations
- Mod. Function And Its Properties
3. Trigonometry
(10 Periods)
- 3.1 Relation Between Sides And Angles Of A Triangle:
- Statement Of Various Formulae Showing Relationship Between Sides And Angle Of A Triangle.
- 3.2 Inverse Circular Functions:
- Simple Case Only
4. Differential Calculus - I
(18 Periods)
- 4.1 Functions, Limits, Continuity:
- Functions And Their Graphs
- Range And Domain
- Elementary Methods Of Finding Limits (Right And Left)
- Elementary Test For Continuity And Differentiability
- 4.2 Methods Of Finding Derivatives:
- Trigonometric Functions
- Exponential Function
- Function Of A Function
- Logarithmic Differentiation
- Differentiation Of Inverse Trigonometric Function
- Differentiation Of Implicit Functions
5. Differential Calculus - II
(18 Periods)
- 5.1
- Higher Order Derivatives
- Leibnitz Theorem (Without Proof)
- Simple Applications
- 5.2 Applications:
- Finding Tangents
- Normal
- Points Of Maxima/Minima
- Increasing/Decreasing Functions
- Rate, Measure, Velocity, Acceleration
- Errors And Approximation
INSTRUCTONAL STRATEGY
The basic instructional strategy to teach basic mathematics, Binomial theorem, trigonometry, differential equations etc. should be conceptual with real world applications of relevant branch. More numerical and theory examples can be used for clear understanding of the content.
MEANS OF ASSESSMENT
- Assignments and Quiz/Class Tests
- Mid-term and End-term Written Tests
- Model/Prototype Making
RECOMMENDED BOOKS
- Elementary Engineering Mathematics by BS Grewal, Khanna Publishers, New Delhi
- Engineering Mathematics, Vol I & II by SS Sastry, Prentice Hall of India Pvt. Ltd
- Applied Mathematics-I by Chauhan and Chauhan, Krishna Publications, Meerut.
- Applied Mathematics-I (A) by Kailash Sinha and Varun Kumar; Aarti Publication, Meerut
Suggested Distribution of Marks
| Topic No. | Time Alloted (Periods) | Marks Allotted (%) |
|---|---|---|
| 1 | 12 | 20 |
| 2 | 12 | 20 |
| 3 | 10 | 12 |
| 4 | 18 | 24 |
| 5 | 18 | 24 |
| Total | 70 | 100 |