Course Content

Other Courses

Tribhuvan university CSIT 2065 Syllabus Calculus and Analytical Geometry

Calculus and Analytical Geometry - Syllabus

Course Overview and Structure
Syllabus Notes Old Questions Unit Wise Questions Question Bank

Embark on a profound academic exploration as you delve into the Calculus and Analytical Geometry course () within the distinguished Tribhuvan university's CSIT department. Aligned with the 2065 Syllabus, this course (MTH-104) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 80+20 marks system, coupled with a challenging passing threshold of , propels students to strive for excellence, fostering a deeper grasp of the course content.

This 3 credit-hour journey unfolds as a holistic learning experience, bridging theory and application. Beyond theoretical comprehension, students actively engage in practical sessions, acquiring valuable skills for real-world scenarios. Immerse yourself in this well-structured course, where each element, from the course description to interactive sessions, is meticulously crafted to shape a well-rounded and insightful academic experience.


Course Synopsis: Preliminaries revision of differentiation and integration; Techniques of integration infinite series; Vectors and analytical geometry in space (differential geometry). Vector valued functions. Multivariable functions and partial derivatives. Multiple integrals and integration in vector fields. Partial derivatives; Equations of First Partial Derivatives.
Goal:  This course aims at providing students with some advanced topics in undergraduate calculus and fundamental concepts of partial differentiation and P.D.E of second order. It is assured that a student who has done Certificate Level papers in mathematics will be able to study this course.

Units

Key Topics

  • Functions and Graphs
    TO-1

    Study of functions and their graphical representations, including domain, range, and composition of functions.

  • Extreme Values of Functions
    TO-2

    Analysis of extreme values of functions, including maxima and minima, and graphing of derivatives.

  • Mean Value Theorem
    TO-3

    Introduction to the Mean Value Theorem, a fundamental concept in differential calculus.

  • Definite Integrals
    TO-4

    Study of definite integrals, including properties, applications, and the Mean Value Theorem for definite integrals.

  • Fundamental Theorem of Integral Calculus
    TO-5

    Exploration of the Fundamental Theorem of Integral Calculus, including its application and improper integrals.

2.1    Infinite sequence and sequence of convergence and divergence                  

2.2    Integral test, comparison test, ratio and root test                 

2.3  Absolute and conditional convergence Power series, Taylor and Maclaurin series, convergence of Taylor series

Key Topics

  • Basic Logic Gates
    CO-01

    This topic covers the fundamental logic gates NOT, OR, and AND, including their symbols, truth tables, and applications.

  • Universal Logic Gates
    CO-02

    This topic explores the universal logic gates NOR and NAND, their properties, and how they can be used to implement other logic gates.

  • EX-OR and EX-NOR Gates
    CO-03

    This topic discusses the EX-OR and EX-NOR gates, their truth tables, and applications in digital circuits.

4.1    Vectors in the space      

4.2    Lines and planes in space          

4.3    Cylinders and Quadric surfaces           

4.4    Cylindrical and Spherical Coordinates

4.5    Vector valued functions and space curves  

4.6    Unit tangent vector, curvature and torsion and TNB system

Key Topics

  • Double Integrals in Rectangular and Polar Coordinates
    MU-5.1

    This topic covers the evaluation of double integrals in rectangular and polar coordinates, including the conversion between the two systems.

  • Applications of Double Integrals
    MU-5.2

    This topic explores the applications of double integrals in finding areas, moments, and center of mass of various regions and objects.

  • Triple Integrals in Rectangular Coordinates
    MU-5.3

    This topic introduces triple integrals in rectangular coordinates and their applications in solving real-world problems.

  • Substitutions in Multiple Integrals
    MU-5.4

    This topic discusses the technique of substitution in multiple integrals, including the use of substitution to simplify complex integrals.

6.1    Functions, limits and continuity of two or more variables  

6.2    Partial derivatives                                                                                             

6.3    Differentiability, Differentials, Total Differential Coefficients

6.4    Directional derivatives and gradient vectors           

6.5    Extreme values     

6.6    Lagrange Multiplies   

7.1    Review of Ordinary Differential Equations                                                     

7.2    Analysis of P.D.E of 1st and 2nd order                                                                 

7.3    Linear equations of the 1st order and the general solutions                                    

7.4    P.D.E of 2nd order, its derivation and basic concepts                                  

7.5    Solution of general P.D.E with constant coefficients, complimentary solution and integral solution        

7.6   Wave equations and heat equations and their solutions (Chapter II, Section 11.1, 11.2, 11.4, 11.5). Erwin and Kreyszig. 8th edition, John-Wiley Publications