Instructor: Hemanshu Kaul
Office: Faculty area, Mumbai Campus.
E-mail: kaul [at] illinoistech.edu

Time:
Section 1 - 11:30am-12:45pm, MWF; Recitation @ 11:30am-12:45pm Tuesday.
Section 2 - 2pm-3:15pm, MWF; Recitation @ 11:30am-12:45pm Thursday.
Place: M05 Mumbai Campus

Office Hours:
Instructor - 10am-11am on Monday & Friday; and by appointment.
Graduate Teaching Assistant - 3:30-4:30pm on Monday & Wednesday; 9:45-11:15am on Wednesday with Aadityaa Dummbala (GTA).
Online TA Tutoring from Chicago - 7:30-9:30pm IST on Thursday with Dulmi Fernando \& Amirreza Eshraghi at Zoom Link.

Textbook:
Calculus Volume 1 at OpenStax.org

My Open Math for HW:
Illinois Tech Math 151 at MyOpenMath.
Use the Course ID and Enrollment Key provided in class to enter this website.

Canvas Page:
Math 151 Section 1 at Canvas
Math 151 Section 2 at Canvas

• Student Self-Study Resources at MyOpenMath. This incudes self-study materials for pre-Calculus including Trigonometry.
• Review of Common Math Errors by Paul Dawkins.
• Review of Algebra and Trigonometry by Paul Dawkins.
• Review Sheets:
  Algebra Review Sheet by Paul Dawkins.
  Trignonometry Review Sheet by Paul Dawkins.

• Monday, Oct 22nd : Exam#2 date has been updated below.


• Monday, Sept 22nd : Exam dates have been announced below.


• Monday, Sept 7th : Check this webpage regularly for announcements, course information, etc.

• Exam #1 : Monday October 12th, during class time. Syllabus: All topics covered from beginning of semester till October 7th, Wednesday,namely Sections 1.1 to 3.2 of the textbook.
• Exam #2 : Wednesday November 18th, during class time. Syllabus: All topics covered from October 7th till November 13th.
• Final Exam : TBA by university. Syllabus: All topics covered during the semester.

• Week #1 : 4 Lectures.
  
  • Topics:Discussion of: Calculus as a disruptive technology and its historical parallels with AI; How is Calculus relevant now; Importance of communication including technical communication; AI and its effect on learning vs AI as a tool; Dangers of applying ideas without understanding them - examples from Calculus and from AI; etc.
    Discussion of class syllabus, structure and purpose.
    Review of functions, well-defined function, domain and range, set and interval notation, creating new functions by algebra and composition, symmetries of functions, polynomials, rational functions, piecewise functions, even/odd functions, transformation of functions, trigonometric functions and identities. (From Sections 1.1-1.4 of the textbook)
    
  • Homework:
    Written HW Assigned at Illinois Tech Math 151 at myopenmath. It is your responsibility to follow the instructions and deadlines for each HW, typically a short HW for each Section.
    Reading HW Read all examples from the relevant sections of the textbook at OpenStax and at MyOpenMath.


• Week #2 : 2 Lectures + 1 Recitation + 1 holiday.
  
  • Topics: Inverse functions, One-to-one functions, graphing inverse functions and finding their domain and range, inverse trigonometric functions and their domain and range; Euler's number, exponential growth, and an application from compounded interest savings, Exponential functions and their properties, Inverse of exponential growth and the log function with different bases, properties of log function. (From Sections 1.4 and 1.5 of the textbook)
    
  • Homework:
    Written HW Assigned at Illinois Tech Math 151 at myopenmath. It is your responsibility to follow the instructions and deadlines for each HW, typically a short HW for each Section.
    Reading HW Read all examples from the relevant sections of the textbook at OpenStax and at MyOpenMath.


• Week #3 : 2 Lectures + 1 Recitation + 1 holiday
  
  • Topics: Completed the discussion of change of base for logarithm. (From Section 1.5)
    Three foundations ideas and questions underlying Calculus - limits/limiting behavior, derivative/instantaneous rate of change, integration/average value; local vs global behavior; applicability of ideas from mathematics, story of Hardy and number theory/eror-correcting codes/crytptographhy. Mysteries of infinity - Hilbert's hotel, etc.
    Limiting behavior with three examples of limits showing three problems with "filling in" the "missing" values from a function (data science perspective); limit and left-side and right side limit; examples with use of numerical values and use of algebra with law of cancellation to show when limit from both directions: (i) exists and is equal, (ii) exists and is not equal, (iii) exists as infinity with vertical asymptote; lim (x-> 0) sin(x)/x and how that allows us to estimate values of sin(x) near zero with x; Infinite limits of the form lim (x ->a) 1/(x-a)^n; Vertical asymptotes.
    Using Laws for algebra of limits under correct conditions to evaluate complicated limits, limits of polynomial and rational functions as evaluation; Evaluating limit sof indeterminate form 0/0 through combination of simplification, cancelation and algebra of limits; Use of conjugate to simplify expressions; Squeeze theorem and finding important trigonometric limits by bounding functions. (From Sections 2.1, 2.2, 2.3 of the textbook)
    
  • Homework:
    Written HW Assigned at Illinois Tech Math 151 at myopenmath. It is your responsibility to follow the instructions and deadlines for each HW, typically a short HW for each Section.
    Reading HW Read all examples from the relevant sections of the textbook at OpenStax and at MyOpenMath. In particular, pay attention to examples of applying Squeeze Theorem.


• Week #4 : 2 Lectures + 1 Recitation + 1 holiday.
  
  • Topics: More examples of Squeeze theorem, Application of Squeeze theorem to find limits as x-> 0, of sin(x), cos(x) using sin(x), sin(x)/x; using rationalization and simplification to reduce triginometric limits to known trigonometric limits.
    Intuitive and formal defintion of continuity of functions using limits, 3-step process for checking continuity at point, How the examples from limits are related to three types of discontinuities - removable, jump and infinite, Extending the definition of continuity to an interval based one-sided limits, Continuity of all polynomials (with proof using algebra of limits) and rational functions, Composite function theorem for computing limit of composition of two functions, Continuity of all trigonometric functions (with proof for continuity of cos(x)), Intermediate Value Theorem and its application to finding roots (zeroes) of a f(x)=0 for any continuous function f, Comment on Global methods and local methods for finding solutions of general equations.
    formal epsilon-delta definition of limit of a function - its meaning using intervals and the importance of "for all epsilon>0" and "there exists delta>0" quantifiers in it, and its translation to the intuitive defintion of limit, Two-step strategy for proving limit of a function to find delta first and then writing the solution. (From Sections 2.3, 2.4 and 2.5 of the textbook)
    
  • Homework:
    Written HW Assigned at Illinois Tech Math 151 at myopenmath. It is your responsibility to follow the instructions and deadlines for each HW, typically a short HW for each Section.
    Reading HW Read all examples from the relevant sections of the textbook at OpenStax and at MyOpenMath.


• Week #5 : 3 Lectures + 1 Recitation.
  
  • Topics: More examples for epsilon-delta proof.
    Motivation and intuition for the derivative of a function using tangent, and instantaneous rate of change. Limit definition of derivative at a point; relation to velocity and rate of change; derivative function and its definition as a limit; different notations for derivative; exchange of information between a function and its derivative using examples and their graphs; Differentiability implies continuity with proof, absolute value function as a counterexample for the converse; examples of non-differentiability with corner, infinite tangent and worse; higher order derivatives na dtheir notation. (From Sections 2.5, 3.1 and 3.2 of the textbook)
    Review for Exam#1.
    
  • Homework:
    Written HW Assigned at Illinois Tech Math 151 at myopenmath. It is your responsibility to follow the instructions and deadlines for each HW, typically a short HW for each Section.
    Reading HW Read all examples from the relevant sections of the textbook at OpenStax and at MyOpenMath.


• Week #6 : 3 Lectures + 1 Exam.
  
  • Topics: Differentiation Rules leading to derivative of polynomials, Algebra of Derivatives with proof, Product rule and its proof, Quotient rule and its proof(s) leading to derivative of all integer powers and rational functions. Linear approximation of differentiable functions with derivative - predicting the future!, Applications/ historical connections to Differentiation and using derivative to describe these phenomenon- motion of particle, population models (and Malthus), Marginal cost, revenue and profit. Derivatives of trigonometric functions - proof of derivative of sin x, using sin x to find derivatives of cos x, tan x, etc, higher order derivatives of sin and cos, periodicity and phase shift by pi/2, and the use of modular arithmetic. (From Sections 3.3, 3.4, 3.5 of the textbook)
    
  • Homework:
    Written HW Assigned at Illinois Tech Math 151 at myopenmath. It is your responsibility to follow the instructions and deadlines for each HW, typically a short HW for each Section.
    Reading HW Read all examples from the relevant sections of the textbook at OpenStax and at MyOpenMath.


• Week #7 : 3 Lectures + 1 Recitation.
  
  • Topics: Discussion of EXAM#1 performance, grading, and solutions.
    Chain rule with its proof through an example, chain rule in combination with other rules and derivatives, Chain rule for composition of 3 or more functions - outside in method, Using chain rule on defintion of inverse function to find rule for differentiating inverse functions, Inverse function theorem and its applications, Power rule for rational exponents, Derivative of inverse of sin with proof, Derivative of inverses of trigonometric functions, An implicit relation between x and y can lead infinitely many functions, Implicit differentiation using chain rule and it applications, Natural exponentiation and log functions, Derivatives of exponentiation and log functions of base e and other bases, Logarithmic differentiation in combination with implicit differentiation. (From Sections 3.6, 3.7, 3.8 and 3.9 of the textbook)
    
  • Homework:
    Written HW Assigned at Illinois Tech Math 151 at myopenmath. It is your responsibility to follow the instructions and deadlines for each HW, typically a short HW for each Section.
    Reading HW Read all examples from the relevant sections of the textbook at OpenStax and at MyOpenMath.