Honors Calculus I
MATH 101-A
Fall ‘23
Class Logistics
Lecture: M-W, 08:00 - 9:15 am
SYLLABUS
LMS Mirror Site: lms.lums.edu.pk
Lectures
Lecture 1: Introduction
Lecture 15: Formal Limits
Lecture 2: Two Basic Problems
Lecture 16: Limit Theorems
Lecture 3: Introduction to Sets
Lecture 17: Squeeze Theorem & Limits
Lecture 4: Induction
Lecture 18: Continuity
Lecture 5: Axioms for the Real Number Field
Lecture 19: Midterm Exam - Solution
Lecture 6: Order Axioms for Real Numbers
Lecture 20: Some Theorems for Continuous Functions
Lecture 7: Properties of Real Numbers
Lecture 21: Introduction to Derivatives
Online Notebook
Video Lecture
Lecture 8: Introduction to Functions
Lecture 22: Derivative Theorems
Lecture 9: Step Functions
Lecture 23: Chain Rule and Implicit Differentiation
Lecture 10: The definite Integral
Lecture 24: Optimization I
Lecture 11: Integrability and Integral as Area
Lecture 25: Optimization II and Mean Value Theorems
Lecture 12: Integrals of Some Functions
Lecture 26: Linear Approximation, Fundamental Theorem of Calculus
Lecture 13: Trig Functions and Integrals
Lecture 27: Some theorems on Integrals
Lecture 14 : Limits: Formal and Informal
Lecture 28: Log and Exponential Functions
Lecture 29: Inverse Trig. Functions, L’Hospital’s Rule
Calculus in Action: Some Applications
Review of Techniques of Integration I
Review of Techniques of Integration II
Homework
Homework 1
Homework 1 Solutions
Homework 2
Homework 2 Solutions
Homework 3
Homework 3 Solutions
Homework 4
Homework 4 Solutions
Past Exams
Midterm 2010
Midterm 2022
Interesting Links
1. 3Blue1Brown - A Graphical Introduction to Calculus
2. Khan Academy Lectures on Calculus
3. Wolframalpha!!
Interesting Readings
1. A Short History of Calculus
2. Countability of Rationals and Uncountability of Reals
3. An Interesting Limit
4. Trigonometric Functions : Sum and Difference
5. Set Theoretic Foundations of Mathematics