Calculus 2 Summer 2025
Calculus 2 Summer 2025
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Schedule:
Mon-Thu 4 00- 5 40 Venue 9B2
Office Hours: 3 00- 4 00 (Mon-Thu) (9-B30 Mathematics Department)
Course Summary
Course Summary
MATH 102: Calculus II is a core course for BS students at LUMS, building on Calculus I (MATH 101). It covers multivariable calculus, vector analysis, and infinite series, with applications in geometry, physics, and engineering.
Grading Breakdown:
Grading Breakdown:
Webwork (15%)
Quizzes (25%)
Midterm Exam (25%) – Closed book, no calculator
Final Exam (35%) – Closed book, no calculator
No Midterm replacement policy
Daily Breakdown: (To be updated daily)
Day 01: Overview of Calculus 2, 3D Coordinate system, Distance Formula, Spheres in n-dimensions.
Day 02: Vectors in R^n, Vector arithmetic and Vector Algebra, Dot Product and its applications.
Day 03: Cross product and its applications, Lines and Planes in 3D.
Day 04: Quadratic Surfaces and their traces.
Day 05: Plane and Space Curves, Vector Functions and their Calculus.
Day 06: More on Curves, Applications of Vector Calculus, Tangents, Normal and Binormals.
Day 07: Arc-length, Curvature and their applications.
Day 08: Functions of several variables, Domain/Range and Contour plots.
Day 09: Limits and Continuity, Partial Derivatives and Tangent Planes.
Day 10: Tangent Planes (continued), Linear Approximations, Differentials, Gradient, Chain Rule.
Day 11: Directional Derivative, Optimization.
Day 12: Lagrange Multipliers, Integrals of Multivariate functions on rectangles, Approximated sums.
Day 13: Iterated integrals, Integrals over general domains. Volume in rectangular coordinates, Fubini's Theorem.
Day 14: Exam Day.
Day 15: Integrals in polar coordinates, Volumes over general regions using rectangular and polar coordinates.
Day 16: Surface Area, Triple integrals, Volume between surfaces, Integration in cylindrical and spherical coordinates.
Day 17: Spherical coordinates continued, General change of variables, Vector Fields, Line integrals of scalar functions.
Day 18: Line integral of Vector fields (Work Done), Conservative Vector fields and potential function, Fundamental Theorem of Line integrals.
Day 19: Green's theorem and its applications, Curl and Divergence (and their applications), Parametric surfaces and Tangent plane on them.
Day 20: Surface area of parametric surfaces, Surface integrals of scalars and vectors (Flux), Stokes and Divergence Theorem.
Day 21: Introduction to sequences, their convergence, continuity theorem, squeeze theorem and monotone convergence theorem, Principle of induction.
Day 22: Introduction to series, Partial sums, Telescoping sums, Geometric series, Divergence Test.
Day 23: Convergence Tests (Integral Test, Basic and Limit Comparison). Alternating series Test, Absolute and conditional convergence. Introduction to Power series (will not be tested).
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