Honors Calculus I

MATH 101-A

Fall ‘23

Instructor: Adnan Khan [Office Hours: T 09:00 - 10:00, F 12:00 – 1:00]

 

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

Online Notebook

Video Lecture

 

 

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