B. Com. (H) Sem I Calculus: Overview
Calculus forms an essential component of the B. Com. (Hons) curriculum at Shri Ram College of Commerce. The subject provides students with the mathematical tools necessary for understanding and analyzing economic concepts and business problems. In Semester I, students are introduced to fundamental elements of calculus including functions, limits, differentiation, integration, and their applications in business and economics.
The tutorial sessions complement theoretical learning by offering hands-on experience with problem-solving techniques. These small-group sessions enable students to work closely with faculty members, clarify doubts, and develop a deeper understanding of mathematical concepts and their practical applications in commerce. Regular practice through tutorial problems enhances analytical skills that are crucial for academic success and future professional endeavors.
The following tutorial list for B. Com. (H) Sem I Calculus is structured to progressively build students' capabilities from basic concepts to more complex applications. Each tutorial focuses on specific topics and includes a range of practice problems designed to reinforce understanding and develop problem-solving proficiency.
Calculus Tutorial List
Tutorial 1: Functions, Limits, and Continuity
Topics Covered:
- Types of functions: algebraic, transcendental, inverse, implicit
- Domain and range determination
- Limits: definitions, techniques of evaluation
- Continuity of functions and discontinuities
- Applications in economics: demand and supply functions
Practice Problems: 18-20 problems focusing on function identification, limit evaluation techniques, and checking continuity of various functions with economic interpretations.
Tutorial 2: Differentiation: Basic Concepts
Topics Covered:
- Definition of derivative from first principles
- Differentiation rules: sum, product, quotient
- Chain rule applications
- Derivatives of standard functions
- Higher order derivatives and their interpretation
Practice Problems: 22 problems applying various differentiation techniques to find first and second-order derivatives of algebraic, exponential, logarithmic, and trigonometric functions.
Tutorial 3: Implicit Differentiation and Related Rates
Topics Covered:
- Implicit differentiation techniques
- Logarithmic differentiation
- Related rates problems
- Applications to business scenarios
- Derivatives of inverse functions
Practice Problems: 20 problems involving implicit differentiation and related rates, including business applications like marginal cost and revenue functions.
Tutorial 4: Applications of Derivatives: Tangents, Normals, and Optimization
Topics Covered:
- Tangents and normals to curves
- L'Hpital's rule and evaluation of limits
- Curve sketching using derivatives
- Monotonicity of functions
- Concavity and points of inflection
Practice Problems: 25 problems covering tangent and normal equations, curve analysis, and interpretation of derivatives in terms of rate of change in business contexts.
Tutorial 5: Applications of Derivatives: Maxima and Minima
Topics Covered:
- Unconstrained optimization problems
- Second derivative test for extrema
- Economic applications: profit maximization, cost minimization, revenue maximization
- Inventory control models
- Elasticity of demand and its relation to derivatives
Practice Problems: 30 optimization problems including revenue maximization, cost minimization, and profit maximization in various business scenarios with economic interpretation.
Tutorial 6: Indefinite Integration
Topics Covered:
- Integration as anti-differentiation
- Basic integration formulas
- Integration by substitution
- Integration by parts
- Integration of rational functions and partial fractions
Practice Problems: 32 integration problems using various techniques, including special substitutions and standard forms of integration.
Tutorial 7: Definite Integration and Applications
Topics Covered:
- Definite integral as a limit of sum
- Fundamental theorem of calculus
- Properties of definite integrals
- Area under curves and between curves
- Improper integrals (basic concepts)
Practice Problems: 25 problems evaluating definite integrals using various techniques and calculating areas under economic functions.
Tutorial 8: Economic Applications of Integration
Topics Covered:
- Consumer surplus and producer surplus calculation
- Total revenue, cost, and profit from marginal functions
- Capital accumulation and investment evaluation
- Lorenz curve and Gini coefficient for income inequality
- Present value and future value calculations
Practice Problems: 22 practical application problems demonstrating how integration is used to calculate economic measures and indices in business contexts.
Tutorial 9: Functions of Several Variables: Partial Derivatives
Topics Covered:
- Functions of two or more variables
- Partial derivatives and their interpretation
- Higher order partial derivatives
- Chain rule for functions of several variables
- Total differentials and approximations
Practice Problems: 24 problems involving partial derivatives of various functions including production functions, utility functions, and profit functions.
Tutorial 10: Homogeneous Functions and Euler's Theorem
Topics Covered:
- Homogeneous functions and degrees
- Euler's theorem for homogeneous functions
- Applications to production functions: returns to scale
- Cost functions and economies of scale
- Income expansion paths
Practice Problems: 18 problems identifying homogeneous functions, applying Euler's theorem, and analyzing returns to scale in production processes.
Tutorial 11: Optimization with Constraints
Topics Covered:
- Constrained optimization problems
- Lagrangian multiplier method
- Applications in consumer theory: utility maximization
- Applications in producer theory: cost minimization
- Substitution effect and income effect
Practice Problems: 20 optimization problems using the Lagrangian multiplier method with economic interpretations of constraints in various business scenarios.
Tutorial 12: Differential Equations and Growth Models
Topics Covered:
- Basic concepts of differential equations
- First order and first degree differential equations
- Solution by separation of variables
- Linear differential equations
- Applications: exponential growth models, market penetration models
Practice Problems: 18 problems solving various types of differential equations and applying them to business growth models, market analysis, and natural resource depletion scenarios.
Tutorial 13: Review and Comprehensive Problem Solving
Topics Covered:
- Integration of concepts across tutorials
- Complex multi-concept problems
- Previous year examination analysis
- Time management in problem-solving
- Strategic approaches to different types of questions
Practice Problems: 35 comprehensive problems covering all topics and their interconnections, with a focus on examination-style questions.
Tutorial Schedule
| Tutorial | Week | Date | Time | Venue |
|---|---|---|---|---|
| Tutorial 1 | Week 1 | July 10 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 2 | Week 2 | July 17 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 3 | Week 3 | July 24 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 4 | Week 4 | July 31 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 5 | Week 5 | August 7 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 6 | Week 6 | August 14 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 7 | Week 7 | August 21 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 8 | Week 8 | August 28 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 9 | Week 9 | September 4 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 10 | Week 10 | September 11 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 11 | Week 11 | September 18 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 12 | Week 12 | September 25 | 2:00 PM - 3:30 PM | Room 301, Main Building |
| Tutorial 13 | Week 13 | October 2 | 2:00 PM - 3:30 PM | Room 301, Main Building |
Recommended References
- B.C. Das and B.N. Mukherjee, "Differential Calculus," U.N. Dhur & Sons Pvt. Ltd., 27th Edition
- B.C. Das and B.N. Mukherjee, "Integral Calculus," U.N. Dhur & Sons Pvt. Ltd., 19th Edition
- Nicholson, W., "Microeconomic Theory: Basic Principles and Extensions," Cengage Learning, 11th Edition
- Chiang, A.C. and Wainwright, K., "Fundamental Methods of Mathematical Economics," McGraw Hill, 4th Edition
- P.M. Chakravarti, "Introductory Mathematics for Commerce," Sultan Chand & Sons, 7th Edition
- K. Sydsaeter and P. Hammond, "Essential Mathematics for Economic Analysis," Pearson, 5th Edition
Important Notes for Students:
- Students should attempt all practice problems before each tutorial session to derive maximum benefit.
- Active participation and discussion in tutorial groups is highly encouraged for better understanding.
- Additional problem sets will be provided through the departmental website for students who need extra practice.
- Regular attendance in tutorials is mandatory as the tutorial carries 15% weightage in the internal assessment.
- Tutorial problem sheets will be uploaded on the departmental website at least one week before the scheduled tutorial.
- Students are encouraged to approach tutors during office hours for clarification of doubts.
- Calculator usage rules as per university examination guidelines must be followed in all tutorial sessions.
