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5c920e9 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 | export const mockCalculusUnit = {
unitId: "calc-u1",
unitTitle: "Limits & Derivatives",
nodes: [
{
id: "calc-n1",
title: "Concept of Limits",
description: "Classify scenarios where limits exist or fail.",
type: "concept",
status: "available",
stages: [
{
stageId: "calc-s1",
topic: "Limit Existence",
module: "Instruction",
component: "TaxonomyMatrix",
skin: "Code",
config: {
data: {
buckets: ["Limit Exists", "Limit Does Not Exist"],
items: [
{ id: "limit1", content: "Left limit = 5, Right = 5" },
{ id: "limit2", content: "Left limit = 3, Right = -3 (Jump)" },
{ id: "limit3", content: "Approaches infinity (Asymptote)" },
{ id: "limit4", content: "Continuous polynomial" }
]
},
initialState: { assignments: {} }
},
validation: { type: "exact", condition: {} },
feedback: {
success: "Excellent classification! Limits require agreement from both sides.",
error: "Check the definitions of jumps and asymptotes.",
hint: "If left and right don't match, it doesn't exist."
}
}
]
},
{
id: "calc-n2",
title: "Derivative Rules",
description: "Match base functions to their derivatives.",
type: "exercise",
status: "locked",
stages: [
{
stageId: "calc-s2",
topic: "Basic Differentiation",
module: "Practice",
component: "PatternMatcher",
skin: "Scientific",
config: {
data: {
pairs: [
{ id: "diff1", left: "f(x) = x³", right: "f'(x) = 3x²" },
{ id: "diff2", left: "f(x) = sin(x)", right: "f'(x) = cos(x)" },
{ id: "diff3", left: "f(x) = eˣ", right: "f'(x) = eˣ" },
{ id: "diff4", left: "f(x) = ln(x)", right: "f'(x) = 1/x" }
]
},
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: {
success: "All matched! You master the basic power and transcendental rules.",
error: "Review your trig and exponential derivatives.",
hint: "The derivative of eˣ is special!"
}
}
]
},
{
id: "calc-n3",
title: "Squeeze Theorem",
description: "Apply the squeeze theorem to find limits.",
type: "concept",
status: "locked",
stages: [
{
stageId: "calc-s3",
topic: "Squeeze Theorem Application",
module: "Instruction",
component: "LogicChain",
skin: "Code",
config: {
data: { nodes: ["Find lower bound g(x)", "Find upper bound h(x)", "Show g(x) ≤ f(x) ≤ h(x)", "Evaluate lim g(x) = lim h(x)", "Conclude lim f(x)"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Perfect squeeze theorem steps!", error: "Review the theorem conditions.", hint: "Both bounds must converge to the same value." }
}
]
},
{
id: "calc-n4",
title: "Continuity",
description: "Determine where functions are continuous.",
type: "exercise",
status: "locked",
stages: [
{
stageId: "calc-s4",
topic: "Continuity Conditions",
module: "Practice",
component: "TaxonomyMatrix",
skin: "Code",
config: {
data: {
buckets: ["Continuous", "Discontinuous"],
items: [
{ id: "cont1", content: "f(a) is defined, lim = f(a)" },
{ id: "cont2", content: "Jump at x = 2" },
{ id: "cont3", content: "Removable hole at x = 0" },
{ id: "cont4", content: "Polynomial on all reals" }
]
},
initialState: { assignments: {} }
},
validation: { type: "exact", condition: {} },
feedback: { success: "Great continuity analysis!", error: "Check the three conditions.", hint: "All three conditions must hold." }
}
]
},
{
id: "calc-n5",
title: "Power Rule",
description: "Master the power rule for differentiation.",
type: "concept",
status: "locked",
stages: [
{
stageId: "calc-s5",
topic: "Power Rule Practice",
module: "Instruction",
component: "LogicChain",
skin: "Code",
config: {
data: { nodes: ["f(x) = xⁿ", "Bring down exponent", "Multiply by coefficient", "Reduce exponent by 1", "f'(x) = nxⁿ⁻¹"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Power rule mastered!", error: "Review the power rule steps.", hint: "d/dx[xⁿ] = nxⁿ⁻¹" }
}
]
},
{
id: "calc-n6",
title: "Product Rule",
description: "Apply the product rule to differentiate.",
type: "exercise",
status: "locked",
stages: [
{
stageId: "calc-s6",
topic: "Product Rule",
module: "Practice",
component: "LogicChain",
skin: "Scientific",
config: {
data: { nodes: ["Identify u and v", "Find u'", "Find v'", "Apply u'v + uv'", "Simplify"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Product rule applied correctly!", error: "Remember: (uv)' = u'v + uv'", hint: "Don't forget both terms." }
}
]
},
{
id: "calc-n7",
title: "Quotient Rule",
description: "Differentiate rational functions.",
type: "concept",
status: "locked",
stages: [
{
stageId: "calc-s7",
topic: "Quotient Rule",
module: "Instruction",
component: "LogicChain",
skin: "Code",
config: {
data: { nodes: ["Identify numerator u", "Identify denominator v", "Compute u'v - uv'", "Divide by v²", "Simplify"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Quotient rule nailed!", error: "Review: (u/v)' = (u'v - uv')/v²", hint: "Lo dHi minus Hi dLo over Lo Lo." }
}
]
},
{
id: "calc-n8",
title: "Chain Rule",
description: "Differentiate composite functions.",
type: "exercise",
status: "locked",
stages: [
{
stageId: "calc-s8",
topic: "Chain Rule",
module: "Practice",
component: "LogicChain",
skin: "Scientific",
config: {
data: { nodes: ["Identify outer function f", "Identify inner function g", "Differentiate f'(g(x))", "Multiply by g'(x)", "Final answer"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Chain rule mastered!", error: "Don't forget the inner derivative!", hint: "d/dx[f(g(x))] = f'(g(x))·g'(x)" }
}
]
},
{
id: "calc-n9",
title: "Implicit Differentiation",
description: "Differentiate implicitly defined functions.",
type: "concept",
status: "locked",
stages: [
{
stageId: "calc-s9",
topic: "Implicit Differentiation Steps",
module: "Instruction",
component: "LogicChain",
skin: "Code",
config: {
data: { nodes: ["Differentiate both sides", "Apply chain rule to y terms", "Collect dy/dx terms", "Factor out dy/dx", "Solve for dy/dx"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Implicit differentiation complete!", error: "Remember to treat y as a function of x.", hint: "Every y term needs dy/dx." }
}
]
},
{
id: "calc-n10",
title: "Related Rates",
description: "Solve related rates problems.",
type: "exercise",
status: "locked",
stages: [
{
stageId: "calc-s10",
topic: "Related Rates Strategy",
module: "Practice",
component: "LogicChain",
skin: "Scientific",
config: {
data: { nodes: ["Draw diagram", "Write equation relating variables", "Differentiate with respect to t", "Substitute known values", "Solve for unknown rate"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Related rates solved!", error: "Make sure to differentiate with respect to time.", hint: "Everything changes with time." }
}
]
},
{
id: "calc-n11",
title: "Trig Derivatives",
description: "Differentiate trigonometric functions.",
type: "concept",
status: "locked",
stages: [
{
stageId: "calc-s11",
topic: "Trig Function Derivatives",
module: "Instruction",
component: "TaxonomyMatrix",
skin: "Code",
config: {
data: {
buckets: ["Positive Cosine Family", "Negative Sine Family"],
items: [
{ id: "trig1", content: "d/dx[sin x] = cos x" },
{ id: "trig2", content: "d/dx[cos x] = -sin x" },
{ id: "trig3", content: "d/dx[tan x] = sec²x" },
{ id: "trig4", content: "d/dx[cot x] = -csc²x" }
]
},
initialState: { assignments: {} }
},
validation: { type: "exact", condition: {} },
feedback: { success: "Trig derivatives classified!", error: "Review co-function patterns.", hint: "Co-functions have negative derivatives." }
}
]
},
{
id: "calc-n12",
title: "Higher-Order Derivatives",
description: "Compute second and third derivatives.",
type: "exercise",
status: "locked",
stages: [
{
stageId: "calc-s12",
topic: "Higher-Order Derivatives",
module: "Practice",
component: "LogicChain",
skin: "Code",
config: {
data: { nodes: ["f(x)", "f'(x) — First derivative", "f''(x) — Second derivative", "f'''(x) — Third derivative"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "Higher-order derivatives done!", error: "Just keep differentiating!", hint: "Differentiate the previous result." }
}
]
},
{
id: "calc-n13",
title: "L'Hôpital's Rule",
description: "Evaluate indeterminate limits.",
type: "concept",
status: "locked",
stages: [
{
stageId: "calc-s13",
topic: "L'Hôpital's Rule",
module: "Instruction",
component: "LogicChain",
skin: "Scientific",
config: {
data: { nodes: ["Check 0/0 or ∞/∞ form", "Differentiate numerator", "Differentiate denominator", "Re-evaluate limit", "Repeat if needed"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "L'Hôpital's applied correctly!", error: "Only works for indeterminate forms.", hint: "Must be 0/0 or ∞/∞ first." }
}
]
},
{
id: "calc-n14",
title: "Mean Value Theorem",
description: "Understand and apply MVT.",
type: "exercise",
status: "locked",
stages: [
{
stageId: "calc-s14",
topic: "MVT Application",
module: "Practice",
component: "LogicChain",
skin: "Code",
config: {
data: { nodes: ["Verify continuity on [a,b]", "Verify differentiability on (a,b)", "Compute [f(b)-f(a)]/(b-a)", "Set f'(c) equal to slope", "Solve for c"] },
initialState: {}
},
validation: { type: "exact", condition: {} },
feedback: { success: "MVT applied perfectly!", error: "Check the theorem conditions.", hint: "There exists a c where the tangent equals the secant." }
}
]
},
{
id: "calc-n15",
title: "Final Challenge",
description: "Comprehensive limits & derivatives assessment.",
type: "challenge",
status: "locked",
stages: [
{
stageId: "calc-s15",
topic: "Comprehensive Review",
module: "Assessment",
component: "TaxonomyMatrix",
skin: "Code",
config: {
data: {
buckets: ["Differentiation Technique", "Limit Technique"],
items: [
{ id: "final1", content: "Chain Rule" },
{ id: "final2", content: "L'Hôpital's Rule" },
{ id: "final3", content: "Product Rule" },
{ id: "final4", content: "Squeeze Theorem" }
]
},
initialState: { assignments: {} }
},
validation: { type: "exact", condition: {} },
feedback: { success: "Congratulations! Calculus mastered!", error: "Review the course material.", hint: "Classify each technique by its primary use." }
}
]
}
]
}; |