Differential Calculus
This course will enable the students to -
- Acquaint the students with fundamental concepts of single variable calculus.
- Explore the solution of problems from a mathematical perspective and help to prepare students to succeed in upper level math, science, engineering and other courses that require calculus.
- Determine whether an infinite series is convergent or divergent.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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CMAT 101
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Differential Calculus (Theory)
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The students will be able to –
CO1: Describe the consequences of Mean Value theorems for differentiable functions and be able to compute the expression for the derivative of curve, pedal equation for Cartesian and Polar curves. CO2: Compute the expression for the derivative of a composite function using the chain rule of differentiation, differentiate a relation implicitly and compute the line tangent to its graph at a point, application of Euler's Theorem in homogeneous functions. CO3: Analyze the extremas of a function on an interval and classify them as minima, maxima, or saddles using the second derivative test. CO4: Determine the chord of curvature, envelopes and asymptotes for polar and cartesian curves. CO5: Compute the convergence of infinite non-negative series and alternative series using various convergence tests. CO6: Interpret the value of the first and second derivative as measures of increase and concavity, convexity of functions; compute the critical points of a function on an interval and be able to trace cartesian and polar curves. |
Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Giving tasks
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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Taylor’s and Maclaurins theorems with different remainders, Expansion of sin(x), cos(x), ex, log(1+x), (1+x)m, Derivative of an arc, Pedal equation (Cartesian and Polar Curves).
Infinite series of non-negative terms, Convergences (definition), Test for Convergence (Without Proof): Comparison test, Cauchy’s nth root test, D’Alembert’s ratio test, Raabe’s test,D’Morgan’s test, Cauchy’s condensation test, Logarithm ratio test, Gauss test. Alternating Series – Leibnitz Test, Absolute and conditional convergence.
Partial differentiation, Total derivative, Euler’s theorem for homogeneous functions, Maxima and minima of functions of two independent variables: necessary and sufficient conditions (without proof), Lagrange’s undetermined multipliers ( without proof ) and related problems.
Radius, center and chord of curvature, Envelopes (Cartesian curves), Asymptotes (Cartesian and Polar curves).
Multiple points, Classification of double points: Node, cusp, point of inflexion, Tracing of Cartesian and polar curves.
- Shanti Narayan, Differential Calculus, S. Chand & Co. Pvt. Ltd. New Delhi, 2008.
- M. Ray and G.C. Sharma, Differential Calculus, Shivalal Agarwal & Co. Agra, 2010.
- Gorakh Prasad, Text Book on Differential Calculus, Pothishala Pvt. Ltd, Allahabad, 2000.
- H.S. Dhami, Differential Calculus, New Age International (P) Ltd., New Delhi, 2012.
- Chaurasia, Goyal, Agarwal, Jain , Differential Calculus, RBD, Jaipur, 2020.
- Schaum’s, Theory and Problems of Advanced Calculus, Schaum’s outline series New York, 2011.
- Ahsan Akhtar and Sabiha Ahsan, A Text Book of Differential Calculus, PHI Ltd. New Delhi, 2009.
- G.N. Berman, A Problem Book in Mathematical Analysis, Mir Publishers, Moscow, 2016.
- G.C. Sharma and Madhu Jain, Calculus, Galgotia Publication, Dariyaganj, New Delhi, 2003.
- Ulrich L. Rohde, G.C. Jain, Ajay K. Poddar and A.K.Ghosh Introduction to Differential Calculus, Wiley Publications USA, 2012.
