Calculus And Analytical Geometry (MTH101) is a fundamental course in mathematics, commonly taught in the first semester of Computer Science and Engineering programs. It provides essential mathematical tools for solving complex problems in various fields, including Computer Science, Physics, and Engineering.
1. Calculus
A) Limits And Continuity
1. Concept of limits
2. Evaluating limits using algebraic techniques
3. Continuity and types of discontinuities B) Differentiation
1. Definition and geometric interpretation of derivatives
2. Differentiation rules: power rule, product rule, quotient rule, chain rule
3. Implicit and logarithmic differentiation
4. Applications:
a. Finding slopes of curves
b. Rate of change
c. Maxima and minima problems C) Integration
1. Definition of integration as the reverse of differentiation
2. Basic integration techniques:
a. Substitution method
b. Integration by parts
c. Partial fraction decomposition
3.Definite and indefinite integrals
4. Applications:
a. Finding area under a curve
b. Calculating volume of solids of revolution
2. Analytical Geometry
A) Coordinate Geometry
1. Definition and geometric interpretation of derivatives
2. Differentiation rules: power rule, product rule, quotient rule, chain rule
3. Implicit and logarithmic differentiation
4. Applications:
a. Finding slopes of curves
b. Rate of change
c. Maxima and minima problems B) Conic Sections
1. Circles: general and standard form of equation
2. Parabola: equation, focus, directrix, and applications
3. Ellipse and hyperbola: standard forms and properties C) Transformations
1. Shifting of axes
2. Rotation of axes
3. Polar coordinates and their conversion
3. Multivariable Calculus (Basic Concepts)
1. Partial differentiation
2. Double and triple integrals
3. Introduction to vector calculus
4. Applications In Computer Science
1. Optimization in algorithms (e.g., gradient descent in machine learning)
2. Computer graphics and 3D modeling
3. Physics simulations in game development
CONCLUSION
This course builds a strong foundation for advanced mathematics and applications in technology-related fields.