Curriculum Syllabus & Outline
Markdown Syllabus# Math 100 Outline
1. Limits & Continuity
2. Derivatives
- Definition, rules (power, product, quotient, chain)
3. Applications of Derivatives
- Related rates, optimization, curve sketching
4. Transcendental Functions
- Trig, exponential, logarithmic derivatives
5. Implicit Differentiation
6. Linear Approximation & Differentials
Educational Context & Standards
Math 100 is first-year differential calculus. Covers limits, derivative rules, and applications including optimization and related rates. Foundation for Math 101/152.
Cross-Curriculum Equivalents
Canada/ON: University of Toronto / Waterloo MAT135 / MATH137
CA-ON-U-CALC1
Canada/AB: University of Alberta MATH 114 / 117
CA-AB-U-CALC1
US/National: AP Calculus AB / BC & Collegiate Calc I
US-AP-CALC-BC
US/NY: SUNY / Columbia Calculus I (MATH UN1101)
US-NY-COL-CALC1
US/TX: UT Austin M 408C / Texas A&M MATH 151
US-TX-UTA-M408
Structured Lesson Modules (6 Lessons)
1
Limits
Evaluate limits algebraically, numerically, graphically. Continuity.
2
Derivative Definition
f'(x)=lim (f(x+h)-f(x))/h. Interpret as slope.
3
Differentiation Rules
Power, sum, product, quotient, chain rules.
4
Transcendentals
Derivatives of sin, cos, e^x, ln x.
5
Applications
Related rates, optimization, curve sketching.
6
Implicit Diff
Differentiate both sides; solve for dy/dx.
Assessments & Check-for-Understanding
Q1
d/dx x^n = ?
Answer
n x^(n-1)
Q2
Derivative of sin x?
Answer
cos x
Q3
Derivative of e^x?
Answer
e^x
Q4
lim x→0 sin x/x?
Answer
1
Q5
Chain rule for f(g(x))?
Answer
f'(g(x)) g'(x)
Q6
Derivative of ln x?
Answer
1/x