Digital Harbor High School – Real Analysis I 405 @ JHU

May 2026 · 2nd Semester

This course is designed to give a firm grounding in the basic tools of analysis. It is recommended as preparation (but may not be a prerequisite) for other advanced analysis courses. Real and complex number systems, topology of metric spaces, limits, continuity, infinite sequences and series, differentiation, Riemann-Stieltjes integration. Prerequisites: Calculus III, Linear Algebra. Topics include: Introduction: The Logic of Quantifiers: Infinite Sets, Proofs, The Rational Number System, The Axiom of Choice Construction of the Real Number System: Cauchy Sequences, The Reals as an Ordered Field, Limits and Completeness Topology of the Real Line: The Theory of Limits, Open Sets and Closed Sets, Compact Sets Continuous Functions: The Concept of Continuity, Properties of Continuous Functions Differential Calculus, Concepts of the Derivative, Properties of the Derivative, Calculus of Derivatives, Higher Derivatives and Taylor’s Theorem Integral Calculus: Integrals of Continuous Functions, The Riemann Integral Sequences and Series of Functions: Complex Numbers, Numerical Series and Sequences, Uniform Convergence, Power Series, Approximation by Polynomials, Equicontinuity Poly Program or AP Capstone | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | | 9th grade | 10th grade | 11th grade | 12th grade | | English I/ English II | English II/ English III | English III or AP Language | English IV or AP Lit | | World History Hon. or AP | American Govt. Hon. or AP | US History or AP | Intro. To Calculus<br>or AP Statistics<br>or AP Calculus AB<br>or AP Calculus BC | | Honors Biology | Chemistry | Physics or AP Physics 1 | | Honors Algebra I <br>or <br>Honors Geometry | Honors Geometry<br>or<br>Honors Algebra II | Honors Algebra II<br>or Pre Calc or AP Pre-Calculus<br>or Intro to Calculus<br>or AP Calculus AB | | Health & Gym | Prob/Stat & Trig | Fine Arts | Elective | | Modern Language | Modern Language | Architecture, Engineering, Construction | Poly Program | AP Capstone | | AP Computer Science | Poly Program | AP Capstone | Poly Program | AP Capstone | Sci Opt = (4)<br>or<br>Engnr Opt = (4) | AP Research = (2) | | Hon. Impact of Tech | Intro to Research | Elective | AP Seminar | Sci Opt = (2)<br>or<br>Engnr Opt = (2) | | 7 credits | 7 credits | 7 credits | 7 credits | Ingenuity Project | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | | 9th grade | 10th grade | 11th grade | 12th grade | | English I | English II | English III or AP Language | English IV or AP Lit | | World History Hon. or AP | American Govt. Hon. or AP | US History or AP | Health II | | Honors Biology | Chemistry / Intro to Research | or AP Chemistry<br>or AP Physics 2 (or E&M)<br>or Honors Physics II | or AP Statistics<br>or AP Calculus AB<br>or AP Calculus BC<br>or DE Linear Algebra 1 & 2 | | ING Honors Geometry<br>or ING Honors Algebra II | ING Honors Algebra II <br>or AP PreCalc<br>or AP Calc AB | AP Pre-Calculus<br>or AP Calculus AB<br>or AP Calc BC | | Health I & Gym | Prob/Stat & Trig | Non-Research | Ing. Research | Non-Research | Ing. Research | Ing. Innovation | | AP Computer Science | AP Physics 1 | Fine Art | Research Practicum (2) | Sci Opt = (3) / (4)<br>or<br>Engr Opt. = (3) / (4) | Sci Opt = (2) / (3)<br>or<br>Engr Opt. = (2) / (3) | Sci Opt = (3) / (4)<br>or<br>Engr Opt. = (3) / (4) | | Elective | | Modern Language | Modern Language | Arch, Engnr, Const | Arch, Engr, Const | Elective | Fine Art | Fine Art | | Elective\* | Elective\* | Elective\* | | Research Pract | | 7 credits | 7 credits | 7 credits | 7 credits | \*dependent on 11th grade science course AJROTC or Band | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | | 9th grade | 10th grade | 11th grade | 12th grade | | English I | English II | English III or AP Language | English IV or AP Lit | | World History Hon. or AP | American Govt. Hon. or AP | US History or AP | Health II | | Honors Biology | Chemistry | Physics or AP Physics 1 | | Honors Algebra I <br>or <br>Honors Geometry | Honors Geometry<br>or<br>Honors Algebra II | Honors Algebra II<br>or Pre-Calc <br>or AP Pre-Calculus<br>or AP Calculus AB | Intro. To Calculus<br>or AP Statistics<br>or AP Calculus AB<br>or AP Calculus BC | | Band | AFJROTC | Band | AFJROTC | Band | AFJROTC | Band | AFJROTC | | AP Computer Science | Aero. Science & Leadership | Prob/Stat & Trig | Band | Aero. Science & Leadership | Band | Aero. Science & Leadership | | Band | Health I & Gym | Band | Aero. Science & Leadership | Health I & Gym | Fine Arts | Sci Opt = (3)<br>or<br>Engnr Opt = (3) | Sci Opt = (3)<br>or<br>Engnr Opt = (3) | | Modern Language | Modern Language | Architecture, Engineering, Construction | Elective | | 7 credits | 7 credits | 7 credits | 7 credits | Project Lead the Way or Computer Science Track | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | | 9th grade | 10th grade | 11th grade | 12th grade | | English I | English II | English III of AP Language | English IV or AP Lit | | Health II | | World History Hon. or AP | American Govt. Hon. or AP | US History or AP | Intro. To Calculus<br>or AP Statistics<br>or AP Calculus AB<br>or AP Calculus BC | | Honors Biology | Chemistry | Physics or AP Physics 1 | | Honors Algebra I <br>or <br>Honors Geometry | Honors Geometry<br>or<br>Honors Algebra II | Honors Algebra II<br>or Pre-Calc or AP Pre-Calculus<br>or AP Calculus AB | | Health & Gym | Prob/Stat & Trig | Fine Arts | | PLTW | CompSci | PLTW | CompSci | PLTW | CompSci | PLTW | CompSci | | Intro Engr Design | AP Computer Science | Princ. of Engineering | AP Comp Sci Principles A | Civil Engnr/Architecture (CEA) | Architecture, Engineering, Construction | Engineering Des & Dev | App Development | | Engnr Opt (3) | Engnr Opt (3) | | Modern Language | Modern Language | Digital Electronics (DE) | Elective | Elective | | 7 credits | 7 credits | 7 credits | 7 credits |