Calculus is a foundational course at SSE; it plays an important role in understanding science, engineering, economics, and computer science, among other disciplines. This introductory calculus course covers differentiation and integration of functions of one variable, with applications.
Class Schedule: [S1] (Tu, Thu 2:00 - 3:15 SDSB B-2), [S4] (Tu, Th 9:30-10:45 SSE 301)(waqas.azhar@lums.edu.pk)
Office Hours:
Instructor's Office Hours: Tu, Thu 11:00 AM-2:00 PM SSE Mathematics Department (9-B30).
TA's Office Hours: TBA
COURSE OUTLINE:
See the course outline and grading policy here.
Past Exams:
Some of the past exams can be found here.
RESOURCES:
For course resources, please click here.
WEEKLY BREAKDOWN:
This portion of the website is to be updated weekly, depending on the topics covered so far. You can find all the lecture pictures here.
WEEK 1: Review of Pre-Calculus, Functions, and their types, and cardinality of sets.
WEEK 2: Introduction to limits, the epsilon-delta definition of limit.
WEEK 3: Limit Laws, Infinite limits, limits at infinity, One-sided limits, asymptotes.
WEEK 4: Continuous functions and their properties. [Continuity, Compact domains]
WEEK 5: Derivatives and their properties. [Der1 , Der2 ]
WEEK 6: Chain rule and Implicit Differentiation. Linear Approximations. [ChainRule, Implicit diff ]
WEEK 7: Related Rates and the nature of the curve. (Related rates.pdf)(Related Rates ) [Nature of the curve ]
WEEK 8: Mean value Theorem, Optimization (Relative and Absolute extrema). [MVT, Optimization ][Optimization cont. ]
MID-TERM (28-10-23)
WEEK 9: Optimization Problems, Antiderivatives. [Optimization+Antiderivatives ]
WEEK 10: Definite integrals as area, Riemann sums.
WEEK 11: Integral as a limit of Riemann sums, Fundamental theorem of Calculus, L'Hopital Rule.
WEEK 12: Fundamental theorem of Calculus II, Area between curves.
WEEK 13: Applications of integration (Arc-length, Mean value theorem for integrals, Velocity-acceleration problems)
WEEK 14: Volumes of Revolution and Goodbyes :-)
EXTRAS: Murder Mysteries and More ... [Slides]
FINAL EXAM (23-12-23)
Solution Key (Might contain some mistakes, feel free to point them out)
GeoGebra:
For graphing and visualization, I recommend the use of GeoGebra and Wolfram Alpha.
Practice Problems:
Practice Problems Link