Curriculum Syllabus & Outline
Markdown Syllabus# Math 151 Outline
1. Limits & Continuity
2. Derivatives (full rules)
3. Applications (optimization, rates)
4. Integration (techniques)
5. Applications of Integration
6. Differential Equations (intro)
7. Sequences & Series (intro)
Educational Context & Standards
Math 151 is an accelerated calculus I course. Covers limits, derivatives, integrals, and applications at a faster pace with more theory.
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 & Continuity
Epsilon-delta intuition. Continuity types.
2
Derivative Rules
All standard rules + implicit.
3
Optimization
Max/min on intervals, global extrema.
4
Integration Techniques
Substitution, by parts, partial fractions.
5
Area & Volume
Between curves, shells, washers.
6
Intro DE
Separable differential equations.
Assessments & Check-for-Understanding
Q1
∫ sin x dx = ?
Answer
-cos x + C
Q2
∫ by parts formula?
Answer
∫u dv = uv - ∫v du
Q3
Derivative of arctan x?
Answer
1/(1+x²)
Q4
Limit x→∞ (1+1/x)^x?
Answer
e
Q5
Second derivative test: f''(c)<0 means?
Answer
Local max
Q6
Solve dy/dx = ky?
Answer
y=Ce^(kx)